Great lesson but on the probability that someone with side effects is male, there seems to an error. The problem comes in when you calculate P(E|S) this should come to 0.07 and not 0.065. Also 0.2*0.7/0.41 = 0.341 and not 0.659 Please correct me if am wrong?
I agree, good video, good demonstration of decision trees, and both of these problems have typos. In the first one, the intermediate typo of 0.065 (should be 0.07) throws off the final answers, which should be: P(male | side effects) = .429 (and P(female| side effects) = .571). In the second problem, everything is correct right up to the end. I believe the answer given is for P(Weak market|negative results of market research) = 0.659, rather than P(Strong market|negative results of market research), which is 0.341.
Excellent explanation from first principles that is much better than most, which treat Bayes as a black box formula. Good also that the answer is scientifically accurate wrt gender. Imagine the contortions necessary if sex was arbitrary and based on self-identification? Statistics would be meaningless if sex were treated as a fiction.
When it says in the problem, "if the market was weak there is a 90% chance the research would indicate so" wouldn't that mean that the probability of it being weak and positive would be 90%? However it says 10% in your first diagram. Maybe I am just stupid, but that doesn't make much sense to me. Is it just an error in the calculations?
If you follow the tree diagram strategy from the first part, than the sum total of all "positive results" seems to mean that the denominator would be: P(All Correct Research Results) = P(Correct|Strong) P(Strong) + P(Correct|Weak) P(Weak) =.80(.70) + .90(.30) = .56 + .27 = .83 At least that's what I think it should be. Maybe that's why I'm struggling with this subject.
A' = nought A or not A? Or nawt A??? With programming we'd say either !A or A = 0 (not A and naught A respectively). Edit: Nevermind. I now see that it's "Not A" ^^
Using Baye’s theorem: P(M|SE) = P(SE|M) * P(M) / (P(SE|M)*P(M) + P(SE|F)* P(F)) --- (1) = 5%*60%/(5%*60% + 4%* 10%) = 3%/7% = 0.42857 or 42.86% is the probability that someone is male given that someone is showing a side effect. Let’s break it down: What % of overall population shows side effect? That is 10% of 40% females = 4% and 5% of 60% males = 3%. So this is total 7%. This is what goes in the denominator of (1) above: P(SE) = P(SE|M)* P(M) + P(SE|F)* P(F). Allow me to take another shot at explaining this without losing our heads in all the formulas. ‘ You have a set of males and females (in a gender binary world). 40% females and 60% males. Of the 40% females 10% have SE. So how many females with SE? 10% of 40% = 4% Similarly how many males with SE? It is given 60% of population is males and 5% of them have SE so 5% * 60% = 3%. So right there you have 3% + 4% = 7% of the overall population that’s showing SE. How many of them is males? We know already that is 5% * 60% = 3%. So of the 7% actually 3% are males. So that’s 3% / 7% or 42.86% is the answer That 3% + 4% is actually the denominator P(SE|M) * P(M) + P(SE|F) * P(F) And 3% is simply P(SE|M) * P(M)
From past experience it is known that a machine if set up correctly 90% of the time, then 95% of good parts are expected but if the machine is not set up correctly then the probability of a good part is only 30%. On a given day the machine is set up and the first component produced was found to be good. What is the probability that the machine is set up correctly?
its always the people who have a pen and paper setup that will save your life thank you very much
I love this video😍. By far the best explanation of how to figure out Bayesian’ theorem.
I totally agree with you. Watched so many videos, but this nailed it for me. Thank you from Zambia.❤
Wonderful presentation. I have understood well the Bayes' Theorem
thanks for the quality understanding for Bayes Theorem.
Well done you have a real knack for that.
Great lesson but on the probability that someone with side effects is male, there seems to an error. The problem comes in when you calculate P(E|S) this should come to 0.07 and not 0.065.
Also 0.2*0.7/0.41 = 0.341 and not 0.659 Please correct me if am wrong?
I agree, good video, good demonstration of decision trees, and both of these problems have typos. In the first one, the intermediate typo of 0.065 (should be 0.07) throws off the final answers, which should be: P(male | side effects) = .429 (and P(female| side effects) = .571). In the second problem, everything is correct right up to the end. I believe the answer given is for P(Weak market|negative results of market research) = 0.659, rather than P(Strong market|negative results of market research), which is 0.341.
Your totally right answer is .07 or 7% chance
probability of being male is 3/7 = 42.85% by my reckoning
AGREE
@@quantquill that’s true👍
Now I get the theorem thanks a lot
I like your strategy ❤️ thank you!
Excellent presentation. It actually makes sesne with the diagrams'
Thanks for this very helpful lesson. Please make more videos on probability. Your explanations are easy to understand
In your first example (0.1x0.4) + (0.05x0.6) = 0.07 not 0.065. In your second example (0.2x0.7)/0.41 = 0.3415 not what you calculate
You are right!
Indeed, this is a great help to teachers of Mathematics.
thanks it was useful ... good job .. keep up the good working
Hi,
Thank you very much.
This helped me resolving my doubts..
Aashay S. (India 🇮🇳 )
Very very helpful thanks :-)
I calculate the probability of being male as 3/7 = 42.86%
Yup, the P(SE) should have come to 0.07, not 0.065
@@EmperorsNewWardrobe Correct.
Node 0: Market State
Edge 0.0 Strong: 70%
→ Node 0.0 Research Result
→ Edge 0.0.0 Positive: 80%
→ Edge 0.0.1 Negative: 20%
Edge 0.1 Weak: 30%
→ Node 0.1 Research Result
→ Edge 0.1.0 Positive: 10%
→ Edge 0.1.1 Negative: 90%
The probability for a positive result:
P(+)
Is the combination of the branches that contain “positive” in the original tree. So in other words:
Edge 0.0 Strong: 70% → Edge 0.0.0 Positive: 80%
and
Edge 0.1 Weak: 30% → Edge 0.1.0 Positive: 10%
Applying the denominator of Bayes' Theorem:
Positive:
P(A|B)P(B) + P(A|!B)P(!B) ⇒
P(+|S)P(S) + P(+|W)P(W) ⇒
P(0.8)P(0.7) + P(0.1)P(0.3) ⇒
(0.8)(0.7)+(0.1)(0.3) ⇒
0.59 = 59%
And thus we automatically know the answer to negative being 41%.
P(S|+) = P(+|S)P(S) / P(+) ⇒
P(S|+) = P(0.8)P(0.7) / P(0.59) ⇒
P(S|+) = (0.8)(0.7) / (0.59) ⇒ 0.949152542 ≈ 0.95
P(S|-) = P(-|S)P(S) / P(-) ⇒
P(S|-) = P(0.2)P(0.7) / P(0.41) ⇒
P(S|-) = (0.2)(0.7) / (0.41) ⇒ 0.341463415 ≈ 0.34
Node 0: Research Result
Edge 0.0: Positive: 59%
→ Node 0.0 Market State
→ Edge 0.0.0 Strong: 95%
→ Edge 0.0.1 Weak: 5%
Edge 0.1: Negative: 41%
→ Node 0.1 Market State
→ Edge 0.1.0 Strong: 34%
→ Edge 0.1.1 Weak: 66%
really helpful, thank you so much for this amazing presentation
extraordinary explanation mam...thank you.
This was really helpful.
Excellent explanation from first principles that is much better than most, which treat Bayes as a black box formula. Good also that the answer is scientifically accurate wrt gender. Imagine the contortions necessary if sex was arbitrary and based on self-identification? Statistics would be meaningless if sex were treated as a fiction.
positive should be 90% and negative should be 10% for the market question
I think there is a problem on the second example, the first tree diagram, the weak part (percentages of indicating and not indicating)
LOVELY.
YOU ARE A HERO not a TEACHER MISS XD
I still don't understand why does the probability change when direction is reversed. Someone please help???
P(a tutorial from you is awesome)=1
thank you
Got 42.86% (!?) in the first problem: 0.03/0.0.3+0.04=0.4285714
agree
When it says in the problem, "if the market was weak there is a 90% chance the research would indicate so" wouldn't that mean that the probability of it being weak and positive would be 90%? However it says 10% in your first diagram. Maybe I am just stupid, but that doesn't make much sense to me. Is it just an error in the calculations?
I thought the same! I think you are right!
I have the same question! @Doulton Wiltshire, Could you please check?
If you follow the tree diagram strategy from the first part, than the sum total of all "positive results" seems to mean that the denominator would be:
P(All Correct Research Results) = P(Correct|Strong) P(Strong) + P(Correct|Weak) P(Weak)
=.80(.70) + .90(.30) = .56 + .27 = .83
At least that's what I think it should be. Maybe that's why I'm struggling with this subject.
for your surprise I was thought the same and looking for comments for confirmation
A' = nought A or not A? Or nawt A??? With programming we'd say either !A or A = 0 (not A and naught A respectively). Edit: Nevermind. I now see that it's "Not A" ^^
Thanks
BTW ATTENTION: THE PROBABILITY OF P(SE) IS NOT 0.065 BUT 0.07!
Using Baye’s theorem: P(M|SE) = P(SE|M) * P(M) / (P(SE|M)*P(M) + P(SE|F)* P(F)) --- (1)
= 5%*60%/(5%*60% + 4%* 10%) = 3%/7% = 0.42857 or 42.86% is the probability that someone is male given that someone is showing a side effect.
Let’s break it down:
What % of overall population shows side effect? That is 10% of 40% females = 4% and 5% of 60% males = 3%.
So this is total 7%.
This is what goes in the denominator of (1) above: P(SE) = P(SE|M)* P(M) + P(SE|F)* P(F).
Allow me to take another shot at explaining this without losing our heads in all the formulas. ‘
You have a set of males and females (in a gender binary world). 40% females and 60% males.
Of the 40% females 10% have SE. So how many females with SE? 10% of 40% = 4%
Similarly how many males with SE? It is given 60% of population is males and 5% of them have SE so 5% * 60% = 3%.
So right there you have 3% + 4% = 7% of the overall population that’s showing SE.
How many of them is males? We know already that is 5% * 60% = 3%. So of the 7% actually 3% are males. So that’s 3% / 7% or 42.86% is the answer
That 3% + 4% is actually the denominator P(SE|M) * P(M) + P(SE|F) * P(F)
And 3% is simply P(SE|M) * P(M)
nice
Your P(SE) should be .07, not .065. The final answer is 3/7 = .429
From past experience it is known that a machine if set up correctly 90% of the time, then 95% of good parts are expected but if the machine is not set up correctly then the probability of a good part is only 30%. On a given day the machine is set up and the first component produced was found to be good. What is the probability that the machine is set up correctly?
The second question confusing!! We don’t even know what we are being ask to look for?? You just started answering
The answer is 42.85% probability not 46.15%.
The presentation is appreciated but the calculation in the first question is way too off.. still good efforts!
First!
Your explanation is very confusing...go and check how @organic chemistry tutor presents
I love the way u teach ma'am 🥹. I understand everything. Much love ❤️