If I had this kind of teacher, maybe it's just me, but I would try to never be late to class. He makes it too interesting and stimulating for me to come late and mis out. Honestly great teaching
Yea this wootube is my crisis fix because my maths teacher has been away for over a month now without any sign of return. Substitutes and stand ins aren’t going to cut it anymore. Also I’m a little betrayed by this because I’m just starting my preliminaries.
I thought that 95% accurate meant that on a hundred of people making the test, 95 get the right answer and 5 get the wrong answer. So when you get positive result you have the 95% of probability that it's right
That’s one way of looking at it. Another way: If 100 person with the disease take the test, we would expect 95 of them to test positive and 5 of them to test negative (even though they have the disease)
It's a bit of a simplified view, because there are two kinds of possible "wrong" answers that a test may give. It could say you're positive when you're not (a false positive) and it could say that you're negative when you're not (a false negative). In reality, those two errors have different rates. For example, a test could be not sensitive enough, and give out many false negatives, but if it say's you're positive you can be sure that it's positive (since you'd be way over the threshold). Taking both of those into account is important, and affects the result. In the example in the video, a test that says "negative" 100% of the time is 99.9% accurate, it will be correct 99.9% of the times, but is also 100% useless in this scenario. The false positives rate will be 0%, the false negatives will be 0.1%, but the true-positive rate will also be 0%. The way I interpret that 95% is that it's both the false-positive rate and the false-negative rate. Which is a simplification but an understandable one :)
For anyone that wants to know how to calculate this. For conditional probability, the equation P(A n B)/P(B) can be used to find the probability of A given B. In our problem, we're looking for the probability of being sick given that a person tested positive. For our problem, this can be written as P(Sick n Correct)/P(Positive). You can also write down P(Sick n Positive)/P(Positive), but I'm writing down P(Sick n Correct) instead in order to distinguish a difference between a positive result and a correct result. First, lets find P(Sick n Correct). For this problem, we assume that the accuracy of the test is independent of the health of the patient. This basically means that being sick or healthy doesn't change the accuracy of the test being correct of incorrect. Since we're assuming independence, P(Sick n Correct) will just be the probability of being sick multiplied by the probability of getting the correct diagnosis (correct diagnosis meaning positive for a sick person). In this case, we get (.001)*(.95)=.00095. For the second part of the problem, we want to find the probability of getting a positive result. There are two possible ways of getting a positive. Either you're sick and got the correct diagnosis, or you're healthy and got the wrong diagnosis. Mathematically, we can write this down as, P(Positive) = P(Sick n Correct)+P(Healthy n Wrong). This would be (.001)*(.95)+(.999)*(.05)= 0.0509. Plugging the numbers into the equation from earlier, we get 0.00095/0.0509=0.01866=1.866%, which is roughly 2%. If you want to solve this by using expected values, in a sample of 10000 people, we would expect 509 people to test as positive. This number comes from using P(Positive)=.0509 , then multiplying it by 10000. Of this 10000, we would also expect 9.5 of these positives to also be true positives.The number comes from P(Sick n Correct)*10000. By doing 9.5/509, you get the same 1.866% from above.
have a huge problem with this video from about 7"'ish. in your reply, you have equated, " given that a person tested positive ", with, " /P(Positive) ". since it is given that the person did test positive so /P(Positive) = 1 not 0.0509 the rest follows all the best
I have seen several videos of this teacher. He normally does a good job explaining. In this particular video I can't help feeling that something went wrong. If the test has a 95% accuracy of being correct, the obvious answer seems to be 95%. But on the other hand we know that we only have a 0.1% chance of having the disease. There is a false zone of 5% and a true zone of 95% regarding the test results. The only factor unknown is, in which of these zones is the person with the disease going to fall, so we should consider two scenarios: 1)- The person with the disease falls in the false zone (5%) 2) - The person with the disease falls in the true zone (95%) If we consider a sample of 1000 people, in the first scenario we have 950 true negatives + 49 false positives + 1 false negative. In the second scenario we have 949 true negatives + 1 true positive + 50 false positives. Since the patient had a positive result we are only interested in finding the chance of true positives against all the positives (being true or false). In the first scenario we don't have any true positives so the probability of having the disease is 0%. In the second scenario we have 1 true positive and 50 false positives, so the probability of having a positive test and actually having the disease (true positive) should be 0.95 * (1/51)= 0.0186274, meaning approximately 1.86 %. Notice that Mr. Woo considered a different scenario, he actually divided (1/50), meaning that he considered the person with the disease to be in the false zone, which would make that person a false negative. Since the patient was diagnosed positive, the scenario presented in this video would be impossible to occur. Overall, the logic is correct, it just failed in the details and the precision of the calculation.
but the probability of him having a positive test is 1 as that is given " ... we know that we only have a 0.1% chance of having the disease ...", this is irrelevant as the question is, " ". it would be relevant if the question was, " What's the chance you have the disease if you had not had a test at all."
2% is not the precise answer. The reason is very simple: there are 2 possibilities that the test result is positive: 1. You are indeed sick, assume the probability of it is P1 2. The test result is wrong, assume tbe probability of it is P2. So the probability that you are indeed sick if the test result is positive is equal to P1/(P1+P2)=95%×0.1%/(95%×0.1%+5%×99.9%)=1.87%
Actually the question wants the probability that the person has the disease given that he/she has tested positive, So the second possibility is not required by the question
In 1000 people, one of them has the disease. Since the question tells us that the person has tested positive, it narrows the pool of people to 50 people only. (In 50 people, one of them has the disease) So the probability that one person has the disease in 50 people is 1/50 or 2%
I think LinZhou is right. Start with 100,000 people. So, 100 are actually sick. 95 sick people test positive (correctly) 5 sick people test negative (incorrectly) 94,905 healthy test negative (correctly) 4,995 healthy test positive (incorrectly) Of the 5,090 people who tested positive, 95 are actually sick = 1.87%
This is not completely correct. If the doctor suspects that you have the disease (as introduced by Eddie), then you cannot be treated as a random individual. If a doctor suspects you have the disease, it changes the probability that you have the disease and you no longer have "0.1%" chance to have the disease. Ask any doctor that suspects someone of a disease...a positive test is not right only 2% of the time. That doesn't make any sense. You have to think about this problem on the condition that the doctor suspected you to begin with. Ironic because this video is titled "Conditional Probability"
Bayes Law. P(A|B) = P(B|A).P(A) / P(B) So the probability of having the disease given a +ve result is 0.95 X 0.001 / (0.95 X 0.001 + 0.05 X 0.999) Which is about 1.866%. The example on the board has missed out false negative results. I recently witnessed this for real. A friend was told they tested positive for a disease even though the doctor thought this was unexpected. A retest with another lab was recommended which came back negative. My friend was really upset and worried waiting for the second set of results. My friend is not mathematical in the least and me explaining Bayes Law didn't really help. The doctor seemed ignorant of it too.
except the answer that mr woo calculated is not answering the question. the prevalence rate in the community is irrelevant to the asked question. with you but the prevalence in the population has no bearing on, "What is the chance of having the disease?'. you only need the 95% accuracy rating. you tested positive > you have an approx. 95% of actually having the disease. if this disease is fatal then you are going to check that your will is in order not go out and celebrate, all the best
Somehow the first run-through of the video went over me pretty quickly and I thought I understood it. However, on my second run-through, I just couldn't wrap my head around the meaning behind the word "accurate." So following Mr. Woo's narrative with the single individual being tested positive for the disease within a population of 1,000 people, would it be reasonable to assume that of the 1,000 people 50 of them had "inaccurate" test results including both false-positive and false-negative results? Since you were tested positive, would that mean the 50 people with "inaccurate" results all be apart of the false-positive group leading to the 1/50 chance of you actually having the disease? If so, then what happened to the false-negative group? Perhaps test inaccuracy also applies to true-positives and true-negatives and I'm just looking at this problem at the wrong angle.
Maybe I'm not sure but, somehow, I actually reckon that the person who is mentioned in this problem is out of the red box. Because: Case 1: If this person is out of red box ( have correct result ), he ( this person ) will have a positive test. In addition, all the people in the red box will have the same one => probability is 1/51 Case 2: If this person is in the red box ( the people who have inaccurate result ), he obviously have the NEGATIVE test. Becasue, in fact, he have a disease and the only one who have a disease in 1000 people. Is it right ??? Hoping for more explanations, please !!!! Thank you^^
5% does not mean the 5% test results has to be “wrong”, it means the test result is not reliable. Otherwise that one person can’t be in the red quadrant since the red quadrant is “all wrong “, because that person is being tested positive where he is actually positive, which means the test result is correct and that means it lies into the 95%
The video is very good. I calculated everything in my notebook and the probability is aproximately 1,8664047%. You just have to divide 0,095% (probability of a true positive) by 5.09% (the probability of a positive, whether the result is accurate or not). He just showed the resolution in a simpler way.
That's what I got, too. He forgot to account for the fact that error can occur in TWO places...in false positives AND in false negatives. He only showed the false positives. He is extremely charismatic, though. I can forgive.
@@renanruseler7455 Hi, I am a little bit curious about why do we have to multiply 1/51 with 0.95 since we have accounted the false positive and true positive which is 50 +1 respectively out from true and false zone on the basis of 95% accuracy of the test?
@@cassierape7243 except mr woo is answering the wrong question. the answer to 'whats the chance you have the disease' is ~95% as the incidence percentage of the disease in the population doesn't affect this question, not relevant all the best
Please make videos on bayes' theorm I have understood the conditional probability but how it works in bayes' theorm I don't get that so please make a video on it!!!
The teacher mentioned symptoms and a raised suspicion in a doctor prior to doing a test. That means the pre-test probability was no longer at the low level of 0.1% background prevalence.
That is why when describing results of diagnostic tests, terminologies such as sensitivity, specificity, false positive rate and false negative rate are used rather than "accuracy". "Accuracy" is a valid scientific term but understanding what's really happening isn't very intuitive. When describing a test result to a patient, former 4 parameters are mainly used rather than accuracy because by definition, those 4 have more straightforward meanings.
confused; the fact that 0.1% of the population are affected does not effect the accuracy of the test on an individual. i comprehend there are false negatives for being told you were positive and false positives for those who are told they do not but the chance you have it given you tested positive must be very high, surely. where am i wrong. any advice appreciated
Was so happy, I wasn't there to shine in ignorance before the students probably less than half my age! Used to read about specificity and sensitivity just towards the exams for safety's sake hoping my short term memory fuse would not blow and hopefully keep it handy for a while before it ended up in my brain's trash bin! Nassim N Taleb caught the medical field people in this similar predicament on probabilities, percentages - and most famously - the P value.
I'm so confused by this, shouldn't the red box be the 5% inaccurate results? If the person who is actually sick is in the red box then that means they got the wrong diagnosis, a false negative. But we're looking for the probability of a true positive.. True/accurate necessarily means the person is outside of the red box right..?
Eddie is wrong here, but i think he knows he is wrong; go to 7:07 as for the correct calculation, sort this comment section by [top comments] and then a user named superdupernice has given that to us
This assumes that the doctor has no idea of who actually has the disease from the symptoms. If the probability of having the disease from the symptoms diagnosed by the doctor was 0.1% was correct, then 2% is correct. The probability of the person having the disease is also a function of the doctor's ability to predict he is correct from the symptoms.
I dont know why you assumed there is a doctor. We just take the test, says nothing about doxtor. Many test you can do yourself. Or in some poor countries, you can have volunteer workers etc. Or you can assume there is a doctor but no symptoms at early stage of disease :P
This is not correct. You said those 50 people are told to have the disease while they are actually healthy; then how can you count the actual unhealthy guy in this 50-people box?! "Accurate" means that the test would be positive if you are unhealthy, or negative if you are healthy. Then you can't add that person to the "inaccurate" box. As a matter of fact, there are 51 people who are told to be sick, of which 50 is because of the 5% inaccuracy and 1 is because of accuracy. then the answer is 1/51 = 1.96%.
Well, that's why there are accepted 5% error in most clinical trials, hyp tests etc. One ill guy would hardly finance pharmacy sector, let's make the test 95% accurate and let in other 49 healthy...
I hate "distractors" on multiple choice tests. In order to get the question right, you first have to pass the test of not getting "distracted" before allowing yourself enough time to fully think about the problem. There is a confirmation trap in seeing the exact answer that you calculated appear in the answer options. While possibly a good life skill, it dilutes the effectiveness of the question at assessing whether or not the student knows the material/correct answer. Ironically, conditionally probability could be applied here.
Hi Eddie, Could you please elaborate on the below concept and how the surprising example can figured out using below formula or suggest how conditional probability plays a role in this ? (posterior odds = prior odds × likelihood ratio )
I wondered when he solves problem.. Not because he solved it but because he was solving without using any theorem and laws.. I think this is called to be good in maths
Im trying to transfer the logic in this example to this question. I just played around with the numbers. Here's the question. Your doctor tells you that there’s a rare disease that affects 4% of the population. He recommends that you take a test. The test is 98% accurate. You test positive on the test. What is the chance that you have the disease?
the test being 98% accurate is an incomplete statement. what does it mean for a test to be 98% accurate?. remember the test gives 2 possible outcomes (positive and negative) so the test has to be accurate in saying " do you have the disease" and "you dont have the disease". in the medical world these are defined as sensitivity and specificity.
We don't know whether the result is false negative so the person can fall into the group of 50 which is false negatice or 950 which are accurate. So, the chance of 1 person being false negative is 2%. That is 2% chance the result is false. Please help me if I haven't understand this correctly.
In 1000 people, we would expect 50 of them test positive. The question states that the test is positive. This means that the doctor must have did the test on one of those 50 people. (SInce the question said that the test is positive) We also know that one in 1000 people has the disease. Since it is given that the person tested positive, that one person with the disease must lie somewhere in the pool of 50 people. In other words, the question wants the probability that out of those 50 people, one of them have the disease. So that is 1/50 or 2%
Drunk Dan But if one of the people in that pool of 50 had the disease the test would have been accurate for that person. Hence the test would not have been 95% accurate but a bit more than that. Going by this logic we would have to have 51 people test positive in this case for the test to completely fulfill the given accuracy. I don’t get how it makes sense to say „Well the test falsely identifies 5% of people so 50/1000 would be positive“ but then count the one who *actually has the disease* into that same group. (Judging by a quick calculation the chance to get a positive result is 5.09% not 5% if this makes my problem with the solution any clearer.)
OMG THIS WAS SO GOOD!!! Here I was suffering over this seemingly dull idea as conditional probability when it can be so intriguing! Thank you for uploading!
If I had this kind of teacher, maybe it's just me, but I would try to never be late to class. He makes it too interesting and stimulating for me to come late and mis out. Honestly great teaching
Sometimes it's very hard to not be late though no matter how hard you try
EpiCuber7 depends where you are prob.
Not only were some late, but some had to be told to take their books out (5:38). They didn’t appreciate the gift they had in this teacher
Yea this wootube is my crisis fix because my maths teacher has been away for over a month now without any sign of return. Substitutes and stand ins aren’t going to cut it anymore. Also I’m a little betrayed by this because I’m just starting my preliminaries.
I thought that 95% accurate meant that on a hundred of people making the test, 95 get the right answer and 5 get the wrong answer. So when you get positive result you have the 95% of probability that it's right
That’s one way of looking at it.
Another way: If 100 person with the disease take the test, we would expect 95 of them to test positive and 5 of them to test negative (even though they have the disease)
It's a bit of a simplified view, because there are two kinds of possible "wrong" answers that a test may give. It could say you're positive when you're not (a false positive) and it could say that you're negative when you're not (a false negative).
In reality, those two errors have different rates. For example, a test could be not sensitive enough, and give out many false negatives, but if it say's you're positive you can be sure that it's positive (since you'd be way over the threshold).
Taking both of those into account is important, and affects the result. In the example in the video, a test that says "negative" 100% of the time is 99.9% accurate, it will be correct 99.9% of the times, but is also 100% useless in this scenario. The false positives rate will be 0%, the false negatives will be 0.1%, but the true-positive rate will also be 0%.
The way I interpret that 95% is that it's both the false-positive rate and the false-negative rate. Which is a simplification but an understandable one :)
For anyone that wants to know how to calculate this.
For conditional probability, the equation P(A n B)/P(B) can be used to find the probability of A given B. In our problem, we're looking for the probability of being sick given that a person tested positive. For our problem, this can be written as P(Sick n Correct)/P(Positive). You can also write down P(Sick n Positive)/P(Positive), but I'm writing down P(Sick n Correct) instead in order to distinguish a difference between a positive result and a correct result.
First, lets find P(Sick n Correct). For this problem, we assume that the accuracy of the test is independent of the health of the patient. This basically means that being sick or healthy doesn't change the accuracy of the test being correct of incorrect. Since we're assuming independence, P(Sick n Correct) will just be the probability of being sick multiplied by the probability of getting the correct diagnosis (correct diagnosis meaning positive for a sick person). In this case, we get (.001)*(.95)=.00095.
For the second part of the problem, we want to find the probability of getting a positive result. There are two possible ways of getting a positive. Either you're sick and got the correct diagnosis, or you're healthy and got the wrong diagnosis. Mathematically, we can write this down as, P(Positive) = P(Sick n Correct)+P(Healthy n Wrong). This would be (.001)*(.95)+(.999)*(.05)= 0.0509.
Plugging the numbers into the equation from earlier, we get 0.00095/0.0509=0.01866=1.866%, which is roughly 2%.
If you want to solve this by using expected values, in a sample of 10000 people, we would expect 509 people to test as positive. This number comes from using P(Positive)=.0509 , then multiplying it by 10000. Of this 10000, we would also expect 9.5 of these positives to also be true positives.The number comes from P(Sick n Correct)*10000. By doing 9.5/509, you get the same 1.866% from above.
This explanation is much more accurate. In the video, Eddie just assumed the doctor's diagnosis was not reliable, which is incorrect.
have a huge problem with this video from about 7"'ish.
in your reply, you have equated, " given that a person tested positive ", with, " /P(Positive) ". since it is given that the person did test positive so /P(Positive) = 1 not 0.0509
the rest follows
all the best
does it mean Eddie's calculation is wrong?
his calculation is simply 1 individual / 50 individuals = 0.02, which is basically 0.1% / (100% - 95%) = 2%
I have seen several videos of this teacher. He normally does a good job explaining. In this particular video I can't help feeling that something went wrong. If the test has a 95% accuracy of being correct, the obvious answer seems to be 95%. But on the other hand we know that we only have a 0.1% chance of having the disease. There is a false zone of 5% and a true zone of 95% regarding the test results. The only factor unknown is, in which of these zones is the person with the disease going to fall, so we should consider two scenarios:
1)- The person with the disease falls in the false zone (5%)
2) - The person with the disease falls in the true zone (95%)
If we consider a sample of 1000 people, in the first scenario we have 950 true negatives + 49 false positives + 1 false negative.
In the second scenario we have 949 true negatives + 1 true positive + 50 false positives.
Since the patient had a positive result we are only interested in finding the chance of true positives against all the positives (being true or false). In the first scenario we don't have any true positives so the probability of having the disease is 0%. In the second scenario we have 1 true positive and 50 false positives, so the probability of having a positive test and actually having the disease (true positive) should be 0.95 * (1/51)= 0.0186274, meaning approximately 1.86 %. Notice that Mr. Woo considered a different scenario, he actually divided (1/50), meaning that he considered the person with the disease to be in the false zone, which would make that person a false negative. Since the patient was diagnosed positive, the scenario presented in this video would be impossible to occur. Overall, the logic is correct, it just failed in the details and the precision of the calculation.
thanks for your nice explanation.
Well explained!!
but the probability of him having a positive test is 1 as that is given
" ... we know that we only have a 0.1% chance of having the disease ...", this is irrelevant as the question is, " ". it would be relevant if the question was, " What's the chance you have the disease if you had not had a test at all."
2% is not the precise answer. The reason is very simple: there are 2 possibilities that the test result is positive: 1. You are indeed sick, assume the probability of it is P1 2. The test result is wrong, assume tbe probability of it is P2. So the probability that you are indeed sick if the test result is positive is equal to P1/(P1+P2)=95%×0.1%/(95%×0.1%+5%×99.9%)=1.87%
The actual answer should be 1/20 * 999 + 1/20 * 1/1000 , right?
Actually the question wants the probability that the person has the disease given that he/she has tested positive, So the second possibility is not required by the question
In 1000 people, one of them has the disease. Since the question tells us that the person has tested positive, it narrows the pool of people to 50 people only. (In 50 people, one of them has the disease)
So the probability that one person has the disease in 50 people is 1/50 or 2%
I think LinZhou is right. Start with 100,000 people. So, 100 are actually sick.
95 sick people test positive (correctly)
5 sick people test negative (incorrectly)
94,905 healthy test negative (correctly)
4,995 healthy test positive (incorrectly)
Of the 5,090 people who tested positive, 95 are actually sick = 1.87%
@@geoffiida3315 Yours is the simplest explanation I could find the entire comment section. Thank you!
This is not completely correct. If the doctor suspects that you have the disease (as introduced by Eddie), then you cannot be treated as a random individual. If a doctor suspects you have the disease, it changes the probability that you have the disease and you no longer have "0.1%" chance to have the disease. Ask any doctor that suspects someone of a disease...a positive test is not right only 2% of the time. That doesn't make any sense. You have to think about this problem on the condition that the doctor suspected you to begin with. Ironic because this video is titled "Conditional Probability"
Bayes Law.
P(A|B) = P(B|A).P(A) / P(B)
So the probability of having the disease given a +ve result is
0.95 X 0.001 / (0.95 X 0.001 + 0.05 X 0.999)
Which is about 1.866%. The example on the board has missed out false negative results.
I recently witnessed this for real. A friend was told they tested positive for a disease even though the doctor thought this was unexpected. A retest with another lab was recommended which came back negative. My friend was really upset and worried waiting for the second set of results. My friend is not mathematical in the least and me explaining Bayes Law didn't really help. The doctor seemed ignorant of it too.
except the answer that mr woo calculated is not answering the question. the prevalence rate in the community is irrelevant to the asked question.
with you but the prevalence in the population has no bearing on, "What is the chance of having the disease?'. you only need the 95% accuracy rating. you tested positive > you have an approx. 95% of actually having the disease. if this disease is fatal then you are going to check that your will is in order not go out and celebrate, all the best
Somehow the first run-through of the video went over me pretty quickly and I thought I understood it. However, on my second run-through, I just couldn't wrap my head around the meaning behind the word "accurate."
So following Mr. Woo's narrative with the single individual being tested positive for the disease within a population of 1,000 people, would it be reasonable to assume that of the 1,000 people 50 of them had "inaccurate" test results including both false-positive and false-negative results? Since you were tested positive, would that mean the 50 people with "inaccurate" results all be apart of the false-positive group leading to the 1/50 chance of you actually having the disease? If so, then what happened to the false-negative group?
Perhaps test inaccuracy also applies to true-positives and true-negatives and I'm just looking at this problem at the wrong angle.
Agrred, he used a poor example to explain conditional probability. There are far simpler and less ambiguous examples out there for this topic.
Thanks for the question. I had the same thought too. I thought I was crazy
That's why you don't use the term "accurate" but "specific" (true negatives) and "sensitive" (true positives).
The answer is not %2. You are wrong.
Maybe I'm not sure but, somehow, I actually reckon that the person who is mentioned in this problem is out of the red box. Because:
Case 1: If this person is out of red box ( have correct result ), he ( this person ) will have a positive test. In addition, all the people in the red box will have the same one => probability is 1/51
Case 2: If this person is in the red box ( the people who have inaccurate result ), he obviously have the NEGATIVE test. Becasue, in fact, he have a disease and the only one who have a disease in 1000 people.
Is it right ??? Hoping for more explanations, please !!!!
Thank you^^
probability and graph matrix set theory.
5% does not mean the 5% test results has to be “wrong”, it means the test result is not reliable.
Otherwise that one person can’t be in the red quadrant since the red quadrant is “all wrong “, because that person is being tested positive where he is actually positive, which means the test result is correct and that means it lies into the 95%
EXACTLY!
I thought the same
The video is very good. I calculated everything in my notebook and the probability is aproximately 1,8664047%. You just have to divide 0,095% (probability of a true positive) by 5.09% (the probability of a positive, whether the result is accurate or not). He just showed the resolution in a simpler way.
That's what I got, too. He forgot to account for the fact that error can occur in TWO places...in false positives AND in false negatives. He only showed the false positives. He is extremely charismatic, though. I can forgive.
@@cassierape7243 Exactly!
@@renanruseler7455 Hi, I am a little bit curious about why do we have to multiply 1/51 with 0.95 since we have accounted the false positive and true positive which is 50 +1 respectively out from true and false zone on the basis of 95% accuracy of the test?
@@cassierape7243 except mr woo is answering the wrong question. the answer to 'whats the chance you have the disease' is ~95% as the incidence percentage of the disease in the population doesn't affect this question, not relevant
all the best
I got 0.018664047151277 also.
Please make videos on bayes' theorm I have understood the conditional probability but how it works in bayes' theorm I don't get that so please make a video on it!!!
How has he only have 999k subs?!? He deserves at least 5million but at least he’s lucky that’s it’s not 666k.
The teacher mentioned symptoms and a raised suspicion in a doctor prior to doing a test. That means the pre-test probability was no longer at the low level of 0.1% background prevalence.
That is why when describing results of diagnostic tests, terminologies such as sensitivity, specificity, false positive rate and false negative rate are used rather than "accuracy". "Accuracy" is a valid scientific term but understanding what's really happening isn't very intuitive. When describing a test result to a patient, former 4 parameters are mainly used rather than accuracy because by definition, those 4 have more straightforward meanings.
I hereby predict that we'll see some goats before this topic is completed :)
i hereby declare that u be quite jk lol
@@Mohammed-pw8un lol
confused; the fact that 0.1% of the population are affected does not effect the accuracy of the test on an individual. i comprehend there are false negatives for being told you were positive and false positives for those who are told they do not but the chance you have it given you tested positive must be very high, surely. where am i wrong. any advice appreciated
For this kind of problem a branching diagram takes away all of the mystery
Litle bit difficult to understand this prob
So conditional probability and bayes theorem is the same thing ?
Was so happy, I wasn't there to shine in ignorance before the students probably less than half my age! Used to read about specificity and sensitivity just towards the exams for safety's sake hoping my short term memory fuse would not blow and hopefully keep it handy for a while before it ended up in my brain's trash bin! Nassim N Taleb caught the medical field people in this similar predicament on probabilities, percentages - and most famously - the P value.
Have you ever read Nassim N Taleb's books? Being a mathematics teacher, I think you may have heard of him.
I'm so confused by this, shouldn't the red box be the 5% inaccurate results? If the person who is actually sick is in the red box then that means they got the wrong diagnosis, a false negative. But we're looking for the probability of a true positive.. True/accurate necessarily means the person is outside of the red box right..?
Eddie is wrong here, but i think he knows he is wrong; go to 7:07
as for the correct calculation, sort this comment section by [top comments] and then a user named superdupernice has given that to us
If you look at the clock on the top of the board, which school doesn’t end at 7:30pm!?!
it's the morning, 7.30am maths. that's why people are late, cause it's the first class of the day
third 9.5%
This assumes that the doctor has no idea of who actually has the disease from the symptoms. If the probability of having the disease from the symptoms diagnosed by the doctor was 0.1% was correct, then 2% is correct. The probability of the person having the disease is also a function of the doctor's ability to predict he is correct from the symptoms.
I dont know why you assumed there is a doctor. We just take the test, says nothing about doxtor. Many test you can do yourself. Or in some poor countries, you can have volunteer workers etc.
Or you can assume there is a doctor but no symptoms at early stage of disease :P
janpawełkubica he does say it’s a doctor. And the doctor thinks it’s possible from symptoms or other traits that the patient has the disease.
This is not correct. You said those 50 people are told to have the disease while they are actually healthy; then how can you count the actual unhealthy guy in this 50-people box?! "Accurate" means that the test would be positive if you are unhealthy, or negative if you are healthy. Then you can't add that person to the "inaccurate" box. As a matter of fact, there are 51 people who are told to be sick, of which 50 is because of the 5% inaccuracy and 1 is because of accuracy. then the answer is 1/51 = 1.96%.
Still confused....if you may please align it with Bay's Theorem....
I have a Proabilities exam in 20 days
You just saved my life
Thank you!!!!!
It is so simple because of you sir
Well, that's why there are accepted 5% error in most clinical trials, hyp tests etc. One ill guy would hardly finance pharmacy sector, let's make the test 95% accurate and let in other 49 healthy...
I hate "distractors" on multiple choice tests. In order to get the question right, you first have to pass the test of not getting "distracted" before allowing yourself enough time to fully think about the problem. There is a confirmation trap in seeing the exact answer that you calculated appear in the answer options. While possibly a good life skill, it dilutes the effectiveness of the question at assessing whether or not the student knows the material/correct answer. Ironically, conditionally probability could be applied here.
Please we need more videos about probability
Hi Eddie,
Could you please elaborate on the below concept and how the surprising example can figured out using below formula or suggest how conditional probability plays a role in this ?
(posterior odds = prior odds × likelihood ratio )
I wondered when he solves problem.. Not because he solved it but because he was solving without using any theorem and laws.. I think this is called to be good in maths
this was brilliant
Best lesson from motivational, full of energy teacher ever!
I want to learn probability and statistics, is there any Eddie Woo playlist for that?
Sir I don't understand..pls explain in board and chake
Meh. I don’t think it’s correct. But i’m only 2% sure.
Congratulations Eddie...I admire your channel. I am an educator as well. Please advise me on how to grow my little channel...Thank you
z probability (dx/dy)z power.
Misleading.
Where are you teaching not as an which state but school system like high school or uni?
Im trying to transfer the logic in this example to this question. I just played around with the numbers. Here's the question.
Your doctor tells you that there’s a rare disease that affects 4% of the population. He recommends that you take a test. The test is 98% accurate. You test positive on the test. What is the chance that you have the disease?
the test being 98% accurate is an incomplete statement. what does it mean for a test to be 98% accurate?. remember the test gives 2 possible outcomes (positive and negative) so the test has to be accurate in saying " do you have the disease" and "you dont have the disease". in the medical world these are defined as sensitivity and specificity.
You are an awesome teacher. Please release your book in india.
I enjoyed this problem. Thanks for sharing it.
We don't know whether the result is false negative so the person can fall into the group of 50 which is false negatice or 950 which are accurate.
So, the chance of 1 person being false negative is 2%. That is 2% chance the result is false.
Please help me if I haven't understand this correctly.
In 1000 people, we would expect 50 of them test positive.
The question states that the test is positive. This means that the doctor must have did the test on one of those 50 people. (SInce the question said that the test is positive)
We also know that one in 1000 people has the disease. Since it is given that the person tested positive, that one person with the disease must lie somewhere in the pool of 50 people.
In other words, the question wants the probability that out of those 50 people, one of them have the disease. So that is 1/50 or 2%
Drunk Dan But if one of the people in that pool of 50 had the disease the test would have been accurate for that person. Hence the test would not have been 95% accurate but a bit more than that.
Going by this logic we would have to have 51 people test positive in this case for the test to completely fulfill the given accuracy.
I don’t get how it makes sense to say „Well the test falsely identifies 5% of people so 50/1000 would be positive“ but then count the one who *actually has the disease* into that same group.
(Judging by a quick calculation the chance to get a positive result is 5.09% not 5% if this makes my problem with the solution any clearer.)
Hi which year you're teaching sir 😍
Ye old Bayesian trap
Beautiful man
very nice
Amazing lesson!
OMG THIS WAS SO GOOD!!! Here I was suffering over this seemingly dull idea as conditional probability when it can be so intriguing! Thank you for uploading!
First
@Jonathan De La Paz 1 = 1^2
@@miikey_lol lol
u r the best mr eddie woo !
u r the best teacher i have come across
Too bad he doesn't teach English!
@@Charles.Wright hehe english is easy though !!
I love you