Thank you for the excellent video! My only criticism is that your analysis presumes that, if there's a 10% chance of wearing red and you wear 10 items of clothing, there's a 100% chance of you wearing red. This is obviously a simplification, in the same sense that tossing two coins doesn't guarantee a 'tails', or that wearing 20 items of clothing doesn't give you a 200% chance (applying sanity checks as suggested) The chance of "wearing red" with ten items is 100% minus the probability of none of the items being red, i.e. 1 - (1-0.1)^10 = 65% (using your assumptions) If people are going to use this approach, I would suggest they explain to the interviewer that it's a rough estimation technique that makes the analysis simpler and is suitable for SMALL values of N (# items worn) only. In the case of 10 items, 65% is very different from 100%. For a smaller value (say, n=3), 27% (correct) is not so different from 30% (incorrect)
David Budden Hi, I think I view this slightly differently. Your calculation assumes AND not OR. Any one piece or more than one piece of clothing could be red. The probability of this is 0.1+0.1+...10 times. 0.1*0.1*0.1... will give you the probability of wearing all pieces of red colour. (1-0.1) is the probability of not wearing a red shirt. (1-0.1) is the probability of not wearing a red pant. Multiplying these two make the two activities dependent. However, these activities are independent (i.e, wearing a red shirt does not determine whether you will wear a red pant or not)
I talked about this problem with my sister, and she pointed out that instead of counting how many times people go out (since that's not really relevant at the beginning of the question) you just count the amount of clothing a person wears in a given day. This means that you would change question 2.2 to "how many clothes do people wear in a single day", this would account for the total amount of clothes that a person changes into, whether they're going out or not. Instead of having "going out twice" the stats would change to "wears x amount of clothing in a given day". So a person who wears four pieces of clothes and changes and wears a different set of four pieces of clothes would be a total of eight pieces of clothing in a day. The chart would probably look more like 5% wears 2 pieces of clothing, 50% wears 4 pieces, 30% wears 6 pieces, and 15% wears 8 pieces or something like that. Then you would just multiply these numbers by the chance of wearing red that day. This way, no one is counted twice, but the idea of wearing more clothes in a day is accounted for. Granted, you would probably have to do more calculations to account for most of the amount of clothing, but it would still make more sense, since "going out" in this question is irrelevant.
Dear Kim, Thank you so much for these lovely videos. It has really helped me clear the prelim interview rounds with almost no other preparation other than your tutorials !Look forward to learning more from you! Regards.
Hi, sorry to write you, but I believe that your reasoning is wrong. If, for example, you have 2 pieces of clothing and the chances of wearing red are 10%, the probability of having something red is equal to P={1 - probability of not having something red}, i.e. 1-(9/10)^2=0.19. Similarly, if you have 5 pieces it will be 1-(9/10)^5=0.41 and if you have 10 pieces it will be 1-(9/10)^10=0.65. This will lead to very different results with a total of 9.18 million instead of your 12.2 million. If you need clarifications let me know. What you are basically saying here with a simpler case is that if I toss a coin 2 times the probability of having at least one head will be 100% (2*50%) that is quite wrong. Please edit the video!!
@fedarduino, could you please explain why you calculate probability of wearing for a single person in this exact way? Why do you use sutraction from 1 and why does the number of clothes pieces go into the power? Will really appreciate an answer
Steven Yu Hi, I believe this is the easiest way to calculate the probability but there could be other ones as well (as a tree diagram for example). In probability when P=1 it means the probability is 100%. In this case, if you want to compute the probability of having something red the easiest way is to compute the probability of not having something red and subtract it from 1. To get this, you just need to multiply your chance of not having something red by itself as many times as the pieces that you have. If you have 3 pieces it will be 9/10*9/10*9/10=(9/10)^3. It's hard to write you the theory behind in a RUclips post, but if you just google 'probability' I am sure you will find a lot more info related to this.
fedarduino Hi fedarduino, I understand where you're coming from but I think the underlying assumption you've made is incorrect. I think the assumption that was made in the video was the probability of "wearing something red" not "having something red". The key assumption here for simplicity is that people would generally own an equal number of pieces of clothing of 10 different colours (i.e 5 white shirts/pants, 5 red shirts/pants, 5 black shirts/pants etc). Therefore, the probability of picking a red shirt is 5 out of 50, which is 10%. You're assumption of "having red" means that people generally own one colour of clothing (i.e one of 10 colours). The two events- wearing a red shirt or wearing a red pant (or both) are independent events and therefore need to be added (i.e 0.1+0.1), not multiplied as (0.1*0.1) will give you the probability of wearing a red shirt and a red pant, which is wrong.
Ankita Mehta Ankita Mehta Ankita Mehta Well, so following your reasoning if someone wears 11 pieces, the probability of wearing one red si 11*0,1 = 1,1. Thats nonsense. If you pick n pieces of clothing randomly, simplifying (we asume after choosing one red the probability of choosing later red again is the same), the probability of choosing at least one red is 1- choosing no red pieces. Choosing no red pieces' probability is 0.9^n (when two events are independent, probabilities are multiplied, no added; for example, probability of having two faces when you throw a coin is 0.5*0.5 not 1). So the probability of wearing AT LEAST one red piece is 1- (0.9)^n.
Completely agree! Though I was doing something wrong, but the calculation is wrong. What they are calculating is the amount of red pieces of clothing, but they are not considering that a person might have 2 or 3 or more pieces of clothing red. Just a quick way to understand that this is wrong. We can review the logic behind the people how go out 2 times. What they are saying in this video is that all of them (100% (10x10%)) will were something red on Mondays. NOT correct. Thanks for leaving this comment. Helps to get it right.
I thought the interviewer said "do not count them twice", so that means in the scenario with people going out twice a day, and each time wearing 5 pieces of clothing, we should simply count it as 5 pieces of clothing and not 10 pieces right?
To be counted in the result as "wearing red", you only need to have one piece of clothing red any time during the day for as little or as long. People going out twice implies that they have changed clothing. Going to work in the morning and maybe out with friends or running errands in the evening. If you're going out a second time, for a different reason, it usually has you dressing differently. That is why "work" only people were counted separately. Now, given that they're changing clothes, it makes them wear 10 pieces a day. Color percentages are kept at the standard 10% for keeping the math simple. Well this is how I feel it should be solved. But it's only guessing and estimation, so feel free to suit it to your own style. Cheers
@@sanmayajolly1225 this is not correct, as person who has went out 4 times will have 200% chance of wearing red, which means that he/she will have 2 pieces of clothing red. This person will be counted twice, even though in clarifications we got the information (indirectly but clearly) that one person that wore any red wordrobe element should be counted once regardless of how many he/she went out. I would say that correct approach would be that chance is 1-(x*p)y where x is number of pieces of clothing, p is probability of choosing red and y is how many times person went out. The solution in video is probably good estimation, but i would like to see way of thinking, rather than result, i would count it as a small error
@@CharioJumpin by this thought process, you could go on to take endless times of going out. 2 times going out was assumed because usually, a person does a complete wardrobe change during 2 major appearances, work and after work. Rest all cases will fall in these 2 categories because if a person steps out 5 times, he/she wont undergo entire wardrobe change all the five times. would be one or two times majorly.
As I have same problem.we can see that the people wearing red when they come out two times is 5 million and the people coming out of the house two time is 5 million this means all people wear red once in 10 dressm.
Your math here is a bit flawed. If a person wears, say, 5 pieces of clothing, the chance that at least one of them will be red is 1-(0.9^5), i.e. one minus the chance none of their clothes is red, which is about 41%. Similarly, if they wear 10 pieces of clothing, their chance will be 1-(0.9^10) which is about 65%.
Absolutely point on! Apart from that, there is one more thing which is wrong. When the guy is multiplying 1 million x 2 pieces x 10%, he is essentially finding the number of pieces which are red and not the number of people. One should understand that when one says 10% (again which is not correct, it should be 19% according to the correct way), we already mean that when 1 million people wear 2 pieces, 10% of those 2 pieces are red meaning 10% of the people are wearing red in some capacity. So, we just need to do 10% of 1 million to find the people. The correct calculation would be: 1 million x 19% for the first part.
Hi Adrian, Thanks for the great question! The short answer is No! You may ask the interviewer these types of input data. Here 's the long answer. So the key to Market-sizing or Guesstimate questions is your methodology of breaking down the big and vague goal into smaller bite-size pieces. So as long as you do that, it's completely ok to ask for data on those bite-size pieces. As a bonus, I will give out a tip you should take when asking for that bite-size pieces (in this case is the NY population). Don't just ask for the data, also tell the interviewer how you (in normal situations) would do to find out about that data. In this particular case, I would say something like: "Now that I have broken down the problem into smaller pieces, I would like to get input data on one of those pieces, the NY population. In real-life situation, I would Google to get it!" Hope this helps! Good luck!
Thanks. If I were really trying to estimate these numbers I would use google to get an estimate of the needed demographic information, so it makes sense that in an interview I would be able to ask for that information.
Thank you very much for the video! I have watched it three times. I was wondering, though, if the set up is fully right. Two things stood out to me: the final number is quite high and we can easily have a number above 20 mln, if we assume a higher number of pieces of clothing. On the first point, the result shows every second person at least would wear something red. Let us walk out and spend an hour. Do you think we would see at least every tenth wearing red? On the second point, if we increase the number of pieces of clothing (which is probably somewhat higher in real life) we can easily have a number above 20 mln. E.g. 5 (at home), 9 (going out once) and 18 (going out twice).
dear Everyone, I know everyone is desperate to apply their calculations correctly, let me tell you this, YOUR RESULT, or IN FACT, THE CALCULATED ESTIMATED RESULT, DOESN'T REALLY MATTER TO THE INTERVIEWER. It's the approach. They aren't trying to judge what probability skills you can flaunt, they're there to judge what sort of approach you have applied. Please Calm down, and try not to focus on the end result! Thank you!
Correct me if I am wrong. I think there is a flaw in your answer. You multiplied %of people*no. of pieces*chances of being red to get the 'no. of people', which is incorrect. Think of it this way - Had there been a total population of 100 people wearing 3 pieces having 100% chances of wearing one piece being red, the answer will yield a total of 300 people wearing red which is greater than the total population! Correct approach should be %of people*chances. The number of pieces should be factored in while calculating the chance of wearing one red.
+Akash Deep Choudhury yeah in your example of 100 people, yeah number of pieces as a factor is incorrect, makes sense, it should rather have been 100 people * % of red per dress [which has 3 pieces having 100 % red which is 3*100% = 3 (being > 1) ==> 100% of dress having red] if 'x' pieces have 60% chance of being red and that turns out to be > 1 it should be considered as 100% of being red in your dress, that was a flaw in the explanation But having this, the approach was good , NYC Population % distribution based on a factor of indoor vs outdoor (more than once included) % of having red in your dress
I tried to answer on my own and I had very similar thinking process, but I used different method to find probability of wearing red. Basically, I just had a glance at some picture of New York, its streets, people in casual clothing in general and found very rough estimation of percentage of people wearing red. Multipled it by people in NYC in total and had my first number. After this I figured I would just keep adding factors like average number of how often people change clothes during a day, how many people would be at work and how it influence their chances of wearing red. For example, some people would definitely wear red if that is the color of their uniforms. And I think people in business suits wear red much rarer nowadays.
The answer is flawed. If people who are going out twice wear 12 pieces instead of 10, we will have the probability of wearing red equal to 120%, which does not make any sense. Actually, the answer shouldn't be using 10*10%; instead, it should be 1-0.9^10 = 0.65.
I agree, it should be 1-0.9^10 for more accurate number. Good catch! But I think Kim just want to simplify the answer. His answer would totally make sense if you assume that people want to wear items with different colors and people also want to have different outfit from each other. 120% should be considered as 100%. people wear 11, 12 piece or more than 10 pieces in general will be counted as wear red. There is no set answer for a guesstimate so you can align with the interviewer to keep your calculation simple. Save your time & effort for other parts. Well, it's more important to grasp the insights Kim shows later in the video. I found it much more meaningful than the example's solution. We will be unlikely to be asked the same question when come to our real interview. Learn the methodology to solve every question, then develop our own answer for each specific question given in real case. Cheers,
Hi, thanks for the excellent video that explains things clearly! I had one question though. I learned that all factors need a logical explanation, but you seem to just make an assumption that 5% of the people stay at home, 75% of the people go out once and 25% of the people go out twice without much explanation. Is a logical explanation unnecessary for this assumption? If so, to what extent do we have to give logical explanation, and to what extent can we just make free guesses?
Been a lifetime member of TRADE WITH LUKASZ WILHELM since November of 2018. I was not convinced that I can succeed as a day trader until I joined HIS COMMUNITY AND GOT THE IQD STRATEGY. Lukasz Wilhelm is the best!!! The learning support system you put together is priceless!
Hi! In the last sector "going out twice" which constitutes 5 million people (or 25% of NY population), the number of people wearing red comes out to be 5 million. Doesn't it seem counter-intuitive? We took a group of 5 million people and our calculation shows that all of them are wearing red.
+Ahsen Parwez I think the way to think about this it is like this. Of those people that go out twice on a Monday in New York in two completely different outfits (10 items), there is a very high chance 1 item will be red. Now this is based on fairly unrealistic %s in a very basic model - but the point of the video is to show a methodology within a time constraint so the actual answer is less important than having a structure in place before calculating it
What would you do in a situation like this if you don't know the popukation of New York? My estimate of the population was way off. Should we just memorize some basic demographic information?
It could help but I wouldn't recommend it. The market-sizing & guesstimate question can be about anything. For example, how many gold balls fit in an airplane??? They don't expect you to memorize the volume an circumference of those things.
don't count them twice, but you counted people wearing red twice at 25%? is this because you assumed people changing into different clothes (different article of red) should be counted twice? I think that number should be halved or this needs clarification as to if different clothes but same person counts as two
I think there's a mistake the author make. When you define "any piece is on a person is red is wearing red". Then, you don't times "# of pieces". Instead, you use 1-prob(not wearing red)^(total piece). Here's an example, your equation will be @home=5%* [1-(1-10%)^(2)]. The illogical part is the author counts 1 person wearing 10 red pieces as 10, which is equal to 10 people with each wearing 1 red piece.
There are sometimes supply side and demand side approaches being mentioned like McDonalds sale on a particular day can be calculated by the supply side or the demand side. Which one to follow when?
Hii, I had a question that what was the role of Monday in the problem which You did not consider in solving the problem. so the first thing that came to my mind was that Monday is a working day , and red is not the color that you generally wear at your workplace and the second thing was that shouldn't we divide it into males and females as it red is considered to be girl's color, and then further divide is working and non working population, Pleas do let me know if I am wrong with my approach. Thank you
I think there is a mistake because, New York population was 19.59million in 2017 and New York City's population is approximately 8 million. So these operations better refer to New York population and not New York City's population. Am i right ?
Where did you get your population figures from? They seemed off to me, and according to The Google, NYC's population is 8 million. There are only 19 million people living in New York state.
No, it's not. NJ has a very large population that isn't located anywhere near NYC. The more accurate way to factor this in is to make an assumption about the commuter population fron NJ, CT and Long Island (which isn't a part of NYC proper and doesn't get counted in statistics, despite having a high commuter population. It's less that the (completely off base) 20 million number matters, more that how you arrived at that number is impractical
0:46 INSANE MUSIC VOLUME, THANKS!! By your algorithm, all 5 million people who GO OUT TWICE must be wearing red... Review your Rule No.3: Is that even reasonable? P(no red for 5 pieces) should be 0.9^5=59%, so P(at least 1 red piece) = 1-0.9^5 = 41%. The second category should be 5.73M, and the third should be 5M * (1-0.9^10) = 3.26M. Final answer: 9.18M in total, or 45.9%.
Hey, nice video. I had a doubt. The question mentioned the number of people wearing red and not the number of red clothing articles that they are wearing. So, should we have multiplied the average number of clothes a person wears to get the final answer ?
Although the structure of the problem is sound the solution is flawed. You are asked to find the number of people wearing red. If someone is wearing 1 piece of red or 5 pieces of red does not matter. It is still 1 person, so multiplying 2 pieces by 10% is completely wrong.
The math here is wrong. Let me elaborate, when you say a guy wear 2 pieces of cloth and the chance for each of them to be red is 10%, the chance for him to wear at least 1 piece of red cloth is (1-(100%-10%)^2). not simply 2*10% as you did in the video. If one follow your calulation, under the 10 piece scenario, then you will have 10*10%=100%, what you saying is if the guy go out twice then he 100% have worn at least 1 piece of red cloth. That is not true, he could have worn the same blue set and going out twice. The actual chance for a 10 pieces guy have worn at least 1 piece in red is (1-(100%-10%)^10), we assume he wears none red at all, the chance is (100%-10%)^10 and then use 1 minus the chance for wearing none red at all.
Do you have a resource or list of numbers we should memorize for estimation type questions (ie. population of the 5 largest countries in the world, population of NYC and LA, volume of a boeing 747, length/width/depth of a standard sedan, height of average skyscraper, etc.)?
I believe you can assume some of these things. Again, its your approach that is important and being tested. No one cares if you know the length of a sedan. As a consultant, flexibility is key. You'll have the data either given to you, or you can GUESSTIMATE.
Thank you so much for sharing. Could you please tell us thatw at is the role of MC delevery associate in Consulting (Accenture) and what kind of questions can be asked in an interview
Let's say the chances of a piece being red is 20%, not 10%... Your answer would be 24.400 million people! How's that math ok? Even if the chances were 100%, your answer could not go over 20 million
+Arthur Lyra other conclusion is that people are wearing more than one piece of red clothing. In this calculation he did not assume that people had to wear only one piece of clothing. I think more than the final number, you have to think outside of the box to draw different conclusions
+lfr0nald0 Yeah, I agree with you that it's necessary to think outside the box to draw different conclusions, but you have to agree with me that the question he had to "answer" was "How many people wear red in New York on a typical Monday?", however he ended up answering "How many red pieces of clothing are worn in New York on a typical Monday?". Can you see that? He was just one step short of answering the actual question, but he didn't.
thanks for explaining the basic but i got stuck when i was solving this problem.. if u could help that willl be great--> Apollo hospital and italy based KOS groups has established a joint venture company ApoKOS in India to address the untapped potential in medical rehablitation services. They jointly launched ApoKOS, first complete rehabilitation hospital with an initial investment of 20 cr. in the 50:50 joint venture. The 64 beded hospital provide complete care for patients suffering from cancer, neurological, orthopedica, caropulmonary, beside trauma care. IT is also equipped with physiotherapy and occupational therapy gyms. ApoKOS plans to expant its network to metropolitan cities. The domestic rehab and physiotherapy market are estimated to be around rs 2,000 cr per annum. Currently the market is concentrated around home and out patient therapy what will be the market size?
Hey Kim, I am trying to guess the market size for a fashion based social network in India. Where and how should I proceed for guesstimating the market size & opportunity ? Thanks.
Hi, In case I don't have any idea about my market size, what should be a approach ? For example you knew about 20 million population which is near true 23 million. For example if someone asks me "Estimate the quantity of wine consumed in Delhi in one year?, what will be an approach and answer ?
Are the 5 articles of clothing the same during summer and winter months, or perhaps 5 articles of clothing is the average of summer and winter months? However, are socks and underwear counted in those 5 articles of clothing? Are accessories like necklaces and bracelets articles of clothing?
If chance is 10% and you got 2 pieces, it should be 1-(1-10%)^2 which is not so much different for 2 pieces, but if you got 10 pieces, then it's way different. If you have 12 pieces, then you are more than for sure wearing red?? No.
If you have two pieces, each has 90% possibility to be NOT red, then the chance that NONE of them is red is 90%^2=81%, instead of 90% x 2 = 180%. As a result, the odds that you have at least one red piece is 1 minus the chance you get something red: 1-90%^2. If you have any questions, please consult any probability textbook around. Probability cannot be more than 1 by definition. I like your videos and hope you consider this seriously.
Sorry bud but Belinda (and many others) are right. Not a big deal. Just goes to show you don't need to be a genius, or even literate in middle school math for that matter, to be a Mckinsey consultant. (Either that or you're not who you say you are.) You seem genuinely confused so I'll make it simpler. If you go into your example and assume everyone in NY wears 12 pieces of clothing (a bad assumption but not technically impossible), you would conclude that more than 20 million people are wearing red. That's not possible.
Your calculation about red is wrong. Other than that, great video. Third group should be named those who went out twice but did not wear red at the first time.
7:50 Apparently your own answer didn't ring any alarm bells in your brain lol, 12.2 million means more than half the people should wear red. Also your approach does not eliminate double counting. If someone wears two or more pieces of red clothing, you count them multiple times. The question doesn't ask how many pieces of clothing worn are red but how many people wear red.
I was asked a ques in my Interview. How many footfalls you are expecting in a marathon organised in your city?? Can you please suggest the solution for it THanks
Hi Runlong Zhao, Mr. Kim and MCP are here all along with your learning process! Should you need any help, don't hesitate to send us messages via live chat at mconsultingprep.com, or by email/FB Messenger!
I am afraid I cannot follow your logic at all. For those who are going out twice, you are saying they have 10 pieces of clothing, with a 10% probability of each being red. Therefore you expect each person to have 1 piece of red clothing on them, which is absurd! You have managed to calculate the pieces of clothing that is red in NYC on a typical Monday (if that), not how many people will wear red.
Thanks for taking out the time to make this video , but I am sorry to say that your calculations are completely wrong and this video needs to be taken down immediately , else you are going to misguide many people out here .I will just point out to one mistake and you can figure out the rest. for @home ppl you say they wear 2 pieces of dress and the chance of the colour is 10%. This means in order to calculate the total number of ppl possibly wearing red is 0.19*5 million. It is 0.19 because you need to calculate the probability of one of the suit pieces being red which has a 0.19 probability assuming only 10 colours are under use.
By that logic, if someone was wearing 10 pieces of clothing then they would have a 100% chance of wearing red. The 19% Ssanvit is referring to is the 20% you calculated (2 pieces x 10% chance of red) minus the chance that both pieces of clothing are red (to avoid double counting, so in this circumstance 10% x 10% = 1%. 20%- 1% = 19%).
The segregation of Population isn't completely Exhaustive. You have only covered people that are staying at home and others who are going out once or twice. But what about the rest of the cases?
You forgot the basics of probability. You should calculate the P(a): The likelihood of a person wearing no red, and then P(b): the likelihood of a person wearing ATLEAST one piece of red is P(b)=1-P(a). Suggest you review the consulting math before misguide people again. Confidence overloaded.
Practice and discuss all the Market-sizing & Guesstimate questions with our community who are learning to master Case Interview: discord.gg/3cTkjZZWhp
Thank you for the excellent video! My only criticism is that your analysis presumes that, if there's a 10% chance of wearing red and you wear 10 items of clothing, there's a 100% chance of you wearing red. This is obviously a simplification, in the same sense that tossing two coins doesn't guarantee a 'tails', or that wearing 20 items of clothing doesn't give you a 200% chance (applying sanity checks as suggested)
The chance of "wearing red" with ten items is 100% minus the probability of none of the items being red, i.e. 1 - (1-0.1)^10 = 65% (using your assumptions)
If people are going to use this approach, I would suggest they explain to the interviewer that it's a rough estimation technique that makes the analysis simpler and is suitable for SMALL values of N (# items worn) only. In the case of 10 items, 65% is very different from 100%. For a smaller value (say, n=3), 27% (correct) is not so different from 30% (incorrect)
David Budden Hi, I think I view this slightly differently. Your calculation assumes AND not OR. Any one piece or more than one piece of clothing could be red. The probability of this is 0.1+0.1+...10 times. 0.1*0.1*0.1... will give you the probability of wearing all pieces of red colour. (1-0.1) is the probability of not wearing a red shirt. (1-0.1) is the probability of not wearing a red pant. Multiplying these two make the two activities dependent. However, these activities are independent (i.e, wearing a red shirt does not determine whether you will wear a red pant or not)
Finally, I saw someone says what I am thinking about.
I talked about this problem with my sister, and she pointed out that instead of counting how many times people go out (since that's not really relevant at the beginning of the question) you just count the amount of clothing a person wears in a given day. This means that you would change question 2.2 to "how many clothes do people wear in a single day", this would account for the total amount of clothes that a person changes into, whether they're going out or not. Instead of having "going out twice" the stats would change to "wears x amount of clothing in a given day". So a person who wears four pieces of clothes and changes and wears a different set of four pieces of clothes would be a total of eight pieces of clothing in a day. The chart would probably look more like 5% wears 2 pieces of clothing, 50% wears 4 pieces, 30% wears 6 pieces, and 15% wears 8 pieces or something like that. Then you would just multiply these numbers by the chance of wearing red that day. This way, no one is counted twice, but the idea of wearing more clothes in a day is accounted for. Granted, you would probably have to do more calculations to account for most of the amount of clothing, but it would still make more sense, since "going out" in this question is irrelevant.
Stupid take
Dear Kim, Thank you so much for these lovely videos. It has really helped me clear the prelim interview rounds with almost no other preparation other than your tutorials !Look forward to learning more from you! Regards.
Hi, sorry to write you, but I believe that your reasoning is wrong.
If, for example, you have 2 pieces of clothing and the chances of wearing red are 10%, the probability of having something red is equal to P={1 - probability of not having something red}, i.e. 1-(9/10)^2=0.19.
Similarly, if you have 5 pieces it will be 1-(9/10)^5=0.41 and if you have 10 pieces it will be 1-(9/10)^10=0.65.
This will lead to very different results with a total of 9.18 million instead of your 12.2 million.
If you need clarifications let me know. What you are basically saying here with a simpler case is that if I toss a coin 2 times the probability of having at least one head will be 100% (2*50%) that is quite wrong.
Please edit the video!!
@fedarduino, could you please explain why you calculate probability of wearing for a single person in this exact way? Why do you use sutraction from 1 and why does the number of clothes pieces go into the power?
Will really appreciate an answer
Steven Yu Hi, I believe this is the easiest way to calculate the probability but there could be other ones as well (as a tree diagram for example). In probability when P=1 it means the probability is 100%. In this case, if you want to compute the probability of having something red the easiest way is to compute the probability of not having something red and subtract it from 1. To get this, you just need to multiply your chance of not having something red by itself as many times as the pieces that you have. If you have 3 pieces it will be 9/10*9/10*9/10=(9/10)^3. It's hard to write you the theory behind in a RUclips post, but if you just google 'probability' I am sure you will find a lot more info related to this.
fedarduino Hi fedarduino, I understand where you're coming from but I think the underlying assumption you've made is incorrect. I think the assumption that was made in the video was the probability of "wearing something red" not "having something red". The key assumption here for simplicity is that people would generally own an equal number of pieces of clothing of 10 different colours (i.e 5 white shirts/pants, 5 red shirts/pants, 5 black shirts/pants etc). Therefore, the probability of picking a red shirt is 5 out of 50, which is 10%. You're assumption of "having red" means that people generally own one colour of clothing (i.e one of 10 colours).
The two events- wearing a red shirt or wearing a red pant (or both) are independent events and therefore need to be added (i.e 0.1+0.1), not multiplied as (0.1*0.1) will give you the probability of wearing a red shirt and a red pant, which is wrong.
Ankita Mehta Ankita Mehta Ankita Mehta Well, so following your reasoning if someone wears 11 pieces, the probability of wearing one red si 11*0,1 = 1,1. Thats nonsense.
If you pick n pieces of clothing randomly, simplifying (we asume after choosing one red the probability of choosing later red again is the same), the probability of choosing at least one red is 1- choosing no red pieces. Choosing no red pieces' probability is 0.9^n (when two events are independent, probabilities are multiplied, no added; for example, probability of having two faces when you throw a coin is 0.5*0.5 not 1). So the probability of wearing AT LEAST one red piece is 1- (0.9)^n.
Completely agree! Though I was doing something wrong, but the calculation is wrong. What they are calculating is the amount of red pieces of clothing, but they are not considering that a person might have 2 or 3 or more pieces of clothing red.
Just a quick way to understand that this is wrong. We can review the logic behind the people how go out 2 times. What they are saying in this video is that all of them (100% (10x10%)) will were something red on Mondays. NOT correct.
Thanks for leaving this comment. Helps to get it right.
I thought the interviewer said "do not count them twice", so that means in the scenario with people going out twice a day, and each time wearing 5 pieces of clothing, we should simply count it as 5 pieces of clothing and not 10 pieces right?
Even I felt the same.
To be counted in the result as "wearing red", you only need to have one piece of clothing red any time during the day for as little or as long. People going out twice implies that they have changed clothing. Going to work in the morning and maybe out with friends or running errands in the evening. If you're going out a second time, for a different reason, it usually has you dressing differently. That is why "work" only people were counted separately.
Now, given that they're changing clothes, it makes them wear 10 pieces a day. Color percentages are kept at the standard 10% for keeping the math simple.
Well this is how I feel it should be solved. But it's only guessing and estimation, so feel free to suit it to your own style.
Cheers
@@sanmayajolly1225 this is not correct, as person who has went out 4 times will have 200% chance of wearing red, which means that he/she will have 2 pieces of clothing red. This person will be counted twice, even though in clarifications we got the information (indirectly but clearly) that one person that wore any red wordrobe element should be counted once regardless of how many he/she went out.
I would say that correct approach would be that chance is 1-(x*p)y where x is number of pieces of clothing, p is probability of choosing red and y is how many times person went out. The solution in video is probably good estimation, but i would like to see way of thinking, rather than result, i would count it as a small error
@@CharioJumpin by this thought process, you could go on to take endless times of going out. 2 times going out was assumed because usually, a person does a complete wardrobe change during 2 major appearances, work and after work. Rest all cases will fall in these 2 categories because if a person steps out 5 times, he/she wont undergo entire wardrobe change all the five times. would be one or two times majorly.
As I have same problem.we can see that the people wearing red when they come out two times is 5 million and the people coming out of the house two time is 5 million this means all people wear red once in 10 dressm.
Your math here is a bit flawed. If a person wears, say, 5 pieces of clothing, the chance that at least one of them will be red is 1-(0.9^5), i.e. one minus the chance none of their clothes is red, which is about 41%. Similarly, if they wear 10 pieces of clothing, their chance will be 1-(0.9^10) which is about 65%.
Absolutely point on! Apart from that, there is one more thing which is wrong. When the guy is multiplying 1 million x 2 pieces x 10%, he is essentially finding the number of pieces which are red and not the number of people. One should understand that when one says 10% (again which is not correct, it should be 19% according to the correct way), we already mean that when 1 million people wear 2 pieces, 10% of those 2 pieces are red meaning 10% of the people are wearing red in some capacity. So, we just need to do 10% of 1 million to find the people. The correct calculation would be: 1 million x 19% for the first part.
Hi Adrian,
Thanks for the great question! The short answer is No! You may ask the interviewer these types of input data.
Here 's the long answer. So the key to Market-sizing or Guesstimate questions is your methodology of breaking down the big and vague goal into smaller bite-size pieces. So as long as you do that, it's completely ok to ask for data on those bite-size pieces.
As a bonus, I will give out a tip you should take when asking for that bite-size pieces (in this case is the NY population). Don't just ask for the data, also tell the interviewer how you (in normal situations) would do to find out about that data. In this particular case, I would say something like:
"Now that I have broken down the problem into smaller pieces, I would like to get input data on one of those pieces, the NY population. In real-life situation, I would Google to get it!"
Hope this helps! Good luck!
Thanks. If I were really trying to estimate these numbers I would use google to get an estimate of the needed demographic information, so it makes sense that in an interview I would be able to ask for that information.
Wow! Absolutely brilliant explanation with visual cues and incredibly helpful.
Thank you very much for the video! I have watched it three times.
I was wondering, though, if the set up is fully right. Two things stood out to me: the final number is quite high and we can easily have a number above 20 mln, if we assume a higher number of pieces of clothing.
On the first point, the result shows every second person at least would wear something red. Let us walk out and spend an hour. Do you think we would see at least every tenth wearing red?
On the second point, if we increase the number of pieces of clothing (which is probably somewhat higher in real life) we can easily have a number above 20 mln. E.g. 5 (at home), 9 (going out once) and 18 (going out twice).
Beautiful breakdown of the guesstimate-solving process. Thank you very much.
Glad you like it^^.
dear Everyone,
I know everyone is desperate to apply their calculations correctly, let me tell you this, YOUR RESULT, or IN FACT, THE CALCULATED ESTIMATED RESULT, DOESN'T REALLY MATTER TO THE INTERVIEWER. It's the approach. They aren't trying to judge what probability skills you can flaunt, they're there to judge what sort of approach you have applied. Please Calm down, and try not to focus on the end result!
Thank you!
Hi I've a suggestion can you please share videos of market forecasting ? This particular example was pretty easy thanks i did watch it several times.
Correct me if I am wrong. I think there is a flaw in your answer. You multiplied %of people*no. of pieces*chances of being red to get the 'no. of people', which is incorrect. Think of it this way - Had there been a total population of 100 people wearing 3 pieces having 100% chances of wearing one piece being red, the answer will yield a total of 300 people wearing red which is greater than the total population! Correct approach should be %of people*chances. The number of pieces should be factored in while calculating the chance of wearing one red.
+Akash Deep Choudhury yeah in your example of 100 people, yeah number of pieces as a factor is incorrect, makes sense, it should rather have been 100 people * % of red per dress [which has 3 pieces having 100 % red which is 3*100% = 3 (being > 1) ==> 100% of dress having red]
if 'x' pieces have 60% chance of being red and that turns out to be > 1 it should be considered as 100% of being red in your dress, that was a flaw in the explanation
But having this, the approach was good ,
NYC Population
% distribution based on a factor of indoor vs outdoor (more than once included)
% of having red in your dress
I tried to answer on my own and I had very similar thinking process, but I used different method to find probability of wearing red.
Basically, I just had a glance at some picture of New York, its streets, people in casual clothing in general and found very rough estimation of percentage of people wearing red. Multipled it by people in NYC in total and had my first number.
After this I figured I would just keep adding factors like average number of how often people change clothes during a day, how many people would be at work and how it influence their chances of wearing red. For example, some people would definitely wear red if that is the color of their uniforms. And I think people in business suits wear red much rarer nowadays.
The answer is flawed. If people who are going out twice wear 12 pieces instead of 10, we will have the probability of wearing red equal to 120%, which does not make any sense. Actually, the answer shouldn't be using 10*10%; instead, it should be 1-0.9^10 = 0.65.
I agree, it should be 1-0.9^10 for more accurate number. Good catch!
But I think Kim just want to simplify the answer. His answer would totally make sense if you assume that people want to wear items with different colors and people also want to have different outfit from each other. 120% should be considered as 100%. people wear 11, 12 piece or more than 10 pieces in general will be counted as wear red. There is no set answer for a guesstimate so you can align with the interviewer to keep your calculation simple. Save your time & effort for other parts.
Well, it's more important to grasp the insights Kim shows later in the video. I found it much more meaningful than the example's solution. We will be unlikely to be asked the same question when come to our real interview. Learn the methodology to solve every question, then develop our own answer for each specific question given in real case.
Cheers,
simple and easy to understand.. Thank you
While solving guesstimates in front of the interviewer, do we talk loudly even while thinking about the answer?
We wanna see more!
Thank you a lot from Russia. Very nice approach which I add to my arsenal,),
Hi, thanks for the excellent video that explains things clearly! I had one question though. I learned that all factors need a logical explanation, but you seem to just make an assumption that 5% of the people stay at home, 75% of the people go out once and 25% of the people go out twice without much explanation. Is a logical explanation unnecessary for this assumption? If so, to what extent do we have to give logical explanation, and to what extent can we just make free guesses?
Been a lifetime member of TRADE WITH LUKASZ WILHELM since November of 2018. I was not convinced that I can succeed as a day trader until I joined HIS COMMUNITY AND GOT THE IQD STRATEGY. Lukasz Wilhelm is the best!!! The learning support system you put together is priceless!
WOW! SUPER AWESOME! And SIMPLE to FOLLOW!!!! You're my hero.
Perfect, the 10% probability reasoning is a killer!!!
Thanks for clarification
Always welcome ^^.
thanks for the simple and structural instructions
Hi,
If we're told to not count people going out twice, why do we include them in our analysis?
Hi, I guess it is just a rational way to categorize people so that we can count the number for each type
Hi! In the last sector "going out twice" which constitutes 5 million people (or 25% of NY population), the number of people wearing red comes out to be 5 million. Doesn't it seem counter-intuitive? We took a group of 5 million people and our calculation shows that all of them are wearing red.
+Ahsen Parwez Guess his "alarm bells" and consistency checks were turned off...
+Ahsen Parwez I think the way to think about this it is like this. Of those people that go out twice on a Monday in New York in two completely different outfits (10 items), there is a very high chance 1 item will be red. Now this is based on fairly unrealistic %s in a very basic model - but the point of the video is to show a methodology within a time constraint so the actual answer is less important than having a structure in place before calculating it
Population of NYC is 8.6MM btw...Population of NY state is around 20MM.
Damn, that's what I thought! Thanks for the clarification - thought I was losing my memory!
What would you do in a situation like this if you don't know the popukation of New York? My estimate of the population was way off. Should we just memorize some basic demographic information?
It could help but I wouldn't recommend it. The market-sizing & guesstimate question can be about anything. For example, how many gold balls fit in an airplane??? They don't expect you to memorize the volume an circumference of those things.
Great session, I really enjoyed it. Thanks
don't count them twice, but you counted people wearing red twice at 25%? is this because you assumed people changing into different clothes (different article of red) should be counted twice? I think that number should be halved or this needs clarification as to if different clothes but same person counts as two
Aakash Mehta the number of pieces are unique
Thank you for this awesome video!!
You are so welcome! Keep crushing it ^^.
I think there's a mistake the author make.
When you define "any piece is on a person is red is wearing red". Then, you don't times "# of pieces". Instead, you use 1-prob(not wearing red)^(total piece). Here's an example, your equation will be @home=5%* [1-(1-10%)^(2)]. The illogical part is the author counts 1 person wearing 10 red pieces as 10, which is equal to 10 people with each wearing 1 red piece.
Check out www.fermiproblems.in/ for a great collection of guesstimates
If they said count someone once what is the purpose of counting people going out twice?
There are sometimes supply side and demand side approaches being mentioned like McDonalds sale on a particular day can be calculated by the supply side or the demand side. Which one to follow when?
NYC population is rather around 8.5 million while the state is about 20 million. Just for information. Doesn't affect the method you demonstrate :)
Good explanation!
Thanks guy, amazing really.
You bet!!!
Hii,
I had a question that what was the role of Monday in the problem which You did not consider in solving the problem.
so the first thing that came to my mind was that Monday is a working day , and red is not the color that you generally wear at your workplace and the second thing was that shouldn't we divide it into males and females as it red is considered to be girl's color, and then further divide is working and non working population, Pleas do let me know if I am wrong with my approach.
Thank you
red is a girl's color? Since when?
I thought that crown is for one and only Pink
I agree with you, I got an answer closer to 2 million people with this approach
In this example, would wearing red underwear count as wearing red? If that's the case the first group of people might be higher.
Hi Kim, thanks for the video. small question- is it not required to state the rationale behind choosing the % of people ate home work etc ?
Shouldn’t we consider the number of tourists visiting the NY Metropolitan area on a typical Monday in addition to the population?
I think there is a mistake because, New York population was 19.59million in 2017 and New York City's population is approximately 8 million. So these operations better refer to New York population and not New York City's population. Am i right ?
Where did you get your population figures from? They seemed off to me, and according to The Google, NYC's population is 8 million. There are only 19 million people living in New York state.
No, it's not. NJ has a very large population that isn't located anywhere near NYC. The more accurate way to factor this in is to make an assumption about the commuter population fron NJ, CT and Long Island (which isn't a part of NYC proper and doesn't get counted in statistics, despite having a high commuter population. It's less that the (completely off base) 20 million number matters, more that how you arrived at that number is impractical
Thank you from China:) !!!
Its really helpful. Thank You.
0:46 INSANE MUSIC VOLUME, THANKS!!
By your algorithm, all 5 million people who GO OUT TWICE must be wearing red... Review your Rule No.3: Is that even reasonable?
P(no red for 5 pieces) should be 0.9^5=59%, so P(at least 1 red piece) = 1-0.9^5 = 41%. The second category should be 5.73M, and the third should be 5M * (1-0.9^10) = 3.26M.
Final answer: 9.18M in total, or 45.9%.
yup, I agree with you.
Could you share that ebook link for case study, Kim?
Hey, nice video. I had a doubt. The question mentioned the number of people wearing red and not the number of red clothing articles that they are wearing. So, should we have multiplied the average number of clothes a person wears to get the final answer ?
Although the structure of the problem is sound the solution is flawed. You are asked to find the number of people wearing red. If someone is wearing 1 piece of red or 5 pieces of red does not matter. It is still 1 person, so multiplying 2 pieces by 10% is completely wrong.
very helpful . thankyou so much
The math here is wrong. Let me elaborate, when you say a guy wear 2 pieces of cloth and the chance for each of them to be red is 10%, the chance for him to wear at least 1 piece of red cloth is (1-(100%-10%)^2). not simply 2*10% as you did in the video. If one follow your calulation, under the 10 piece scenario, then you will have 10*10%=100%, what you saying is if the guy go out twice then he 100% have worn at least 1 piece of red cloth. That is not true, he could have worn the same blue set and going out twice. The actual chance for a 10 pieces guy have worn at least 1 piece in red is (1-(100%-10%)^10), we assume he wears none red at all, the chance is (100%-10%)^10 and then use 1 minus the chance for wearing none red at all.
What is a good source to think through different questions to get a flair of guessing and estimating within order?
What does going out have anything to do about it??
Going out wear 5/10 pieces as opposed to staying home wearing 2 pieces. So chances of finding red are high among people going out
nice video. I liked it :)
nice comment. I liked it!
Do you have a resource or list of numbers we should memorize for estimation type questions (ie. population of the 5 largest countries in the world, population of NYC and LA, volume of a boeing 747, length/width/depth of a standard sedan, height of average skyscraper, etc.)?
I believe you can assume some of these things. Again, its your approach that is important and being tested. No one cares if you know the length of a sedan. As a consultant, flexibility is key. You'll have the data either given to you, or you can GUESSTIMATE.
Thank you so much for sharing. Could you please tell us thatw at is the role of MC delevery associate in Consulting (Accenture) and what kind of questions can be asked in an interview
Hi, Should we take into aacount Why people tend to wear red dress?? Like if its valentines day or Christmas ?
Wao!! Thanks a lot!
Can you bring a calculator to the interview?
How did you manage to come with the percentages like 10% wears Red & 5% sit at home, etc. That does not make any sense.
Let's say the chances of a piece being red is 20%, not 10%...
Your answer would be 24.400 million people!
How's that math ok?
Even if the chances were 100%, your answer could not go over 20 million
+Arthur Lyra other conclusion is that people are wearing more than one piece of red clothing. In this calculation he did not assume that people had to wear only one piece of clothing. I think more than the final number, you have to think outside of the box to draw different conclusions
+lfr0nald0 Yeah, I agree with you that it's necessary to think outside the box to draw different conclusions, but you have to agree with me that the question he had to "answer" was "How many people wear red in New York on a typical Monday?", however he ended up answering "How many red pieces of clothing are worn in New York on a typical Monday?".
Can you see that? He was just one step short of answering the actual question, but he didn't.
I agree with you. Had I been the evaluator I would not have passed the candidate.
thanks for explaining the basic but i got stuck when i was solving this problem.. if u could help that willl be great--> Apollo hospital and italy based KOS groups has established a joint venture company ApoKOS in India to address the untapped potential in medical rehablitation services. They jointly launched ApoKOS, first complete rehabilitation hospital with an initial investment of 20 cr. in the 50:50 joint venture. The 64 beded hospital provide complete care for patients suffering from cancer, neurological, orthopedica, caropulmonary, beside trauma care. IT is also equipped with physiotherapy and occupational therapy gyms. ApoKOS plans to expant its network to metropolitan cities. The domestic rehab and physiotherapy market are estimated to be around rs 2,000 cr per annum. Currently the market is concentrated around home and out patient therapy what will be the market size?
Thanks!
You bet!
Hey Kim, I am trying to guess the market size for a fashion based social network in India. Where and how should I proceed for guesstimating the market size & opportunity ?
Thanks.
Hi, In case I don't have any idea about my market size, what should be a approach ? For example you knew about 20 million population which is near true 23 million. For example if someone asks me "Estimate the quantity of wine consumed in Delhi in one year?, what will be an approach and answer ?
Maths was never the focus, the apporoach was.
Awsome
Thanks ^^
The intro music is too loud...
Noted for improvements! Thanks for your comment!
NYC population is 8 mln, not 20mln, which is for New York state. But thanks for the framework and approach!
You bet ^^
1st of all video has cleared all my doubts
having one problem
I can't find link for e book of case studies .
will you share it again?
Read "Case in Point". It will help.
Thank you!
ThanQ
very helpful
Cool video
Cool comment
Are the 5 articles of clothing the same during summer and winter months, or perhaps 5 articles of clothing is the average of summer and winter months?
However, are socks and underwear counted in those 5 articles of clothing? Are accessories like necklaces and bracelets articles of clothing?
Check out www.fermiproblems.in/ for a great collection of guesstimates
What does going out twice here mean?
If chance is 10% and you got 2 pieces, it should be 1-(1-10%)^2 which is not so much different for 2 pieces, but if you got 10 pieces, then it's way different. If you have 12 pieces, then you are more than for sure wearing red?? No.
If you have two pieces, each has 90% possibility to be NOT red, then the chance that NONE of them is red is 90%^2=81%, instead of 90% x 2 = 180%. As a result, the odds that you have at least one red piece is 1 minus the chance you get something red: 1-90%^2.
If you have any questions, please consult any probability textbook around. Probability cannot be more than 1 by definition. I like your videos and hope you consider this seriously.
Sorry bud but Belinda (and many others) are right. Not a big deal. Just goes to show you don't need to be a genius, or even literate in middle school math for that matter, to be a Mckinsey consultant. (Either that or you're not who you say you are.)
You seem genuinely confused so I'll make it simpler. If you go into your example and assume everyone in NY wears 12 pieces of clothing (a bad assumption but not technically impossible), you would conclude that more than 20 million people are wearing red. That's not possible.
Your calculation about red is wrong. Other than that, great video. Third group should be named those who went out twice but did not wear red at the first time.
7:50 Apparently your own answer didn't ring any alarm bells in your brain lol, 12.2 million means more than half the people should wear red. Also your approach does not eliminate double counting. If someone wears two or more pieces of red clothing, you count them multiple times. The question doesn't ask how many pieces of clothing worn are red but how many people wear red.
Finally someone who saw the 2nd problem of the reasoning.
Hi Kim, is this you, who was talking in the video?
Hi Ngoc Vinh Nguyen, does it matter anyway? Hope you learn from our videos ^^
I was asked a ques in my Interview.
How many footfalls you are expecting in a marathon organised in your city??
Can you please suggest the solution for it
THanks
90000 i think
I didn't got the point 2.1 going out once 5 pieces. What does it mean ?
Because i think here means one people go outside with 5 clothing (one red t-shirt, one red pants, one red underwear) ????
Awesome
Hopefully our video helps! You may want to read our articles on the same topic at mconsultingprep.com/case-interview-market-sizing-guesstimate/
How do I estimate how many people are going to diagnostic lab in a day in Kerala?
Show me how you do it ^^.
figures like NY population being 20mn are tricky....we need to know realistic assumptions here....any pointers? Why 20 mn?
+MConsulting Prep Alright, Many Thanks.
Hi Kim, you still working on MCP?
Hi Runlong Zhao, Mr. Kim and MCP are here all along with your learning process! Should you need any help, don't hesitate to send us messages via live chat at mconsultingprep.com, or by email/FB Messenger!
12.5 million out of 20 seems ver unrealistic considering how uncommon red is as a clothing colour
(you spelled hassle wrong - it shows hustle in the video btw)
I think 12M out of 20M is high but otherwise good case
New york city population is 8m lol. 20m is the state.
6:44
mistake alert! please redo the math...
I am afraid I cannot follow your logic at all. For those who are going out twice, you are saying they have 10 pieces of clothing, with a 10% probability of each being red. Therefore you expect each person to have 1 piece of red clothing on them, which is absurd! You have managed to calculate the pieces of clothing that is red in NYC on a typical Monday (if that), not how many people will wear red.
Thanks for taking out the time to make this video , but I am sorry to say that your calculations are completely wrong and this video needs to be taken down immediately , else you are going to misguide many people out here .I will just point out to one mistake and you can figure out the rest. for @home ppl you say they wear 2 pieces of dress and the chance of the colour is 10%. This means in order to calculate the total number of ppl possibly wearing red is 0.19*5 million. It is 0.19 because you need to calculate the probability of one of the suit pieces being red which has a 0.19 probability assuming only 10 colours are under use.
By that logic, if someone was wearing 10 pieces of clothing then they would have a 100% chance of wearing red. The 19% Ssanvit is referring to is the 20% you calculated (2 pieces x 10% chance of red) minus the chance that both pieces of clothing are red (to avoid double counting, so in this circumstance 10% x 10% = 1%. 20%- 1% = 19%).
The segregation of Population isn't completely Exhaustive. You have only covered people that are staying at home and others who are going out once or twice. But what about the rest of the cases?
NYC population is 8m. 🙄
I'm really confused now!!!
The only way to master this type of question is to practice. Check it out mconsultingprep.com/market-sizing-example/!
Check out www.fermiproblems.in/ for a great collection of guesstimates
You forgot the basics of probability. You should calculate the P(a): The likelihood of a person wearing no red, and then P(b): the likelihood of a person wearing ATLEAST one piece of red is P(b)=1-P(a).
Suggest you review the consulting math before misguide people again. Confidence overloaded.
ruclips.net/video/xesdOE4aPKM/видео.html any different method for this
6:39 all 5 million people going out twice are wearing red...? Think you need to go back to statistics class!