Conditional Probability question

#3
Almost no math needed here. It gave you the true-positive probability of the test, 91%. Its asking you what is the false-positive probability of the test. The probability of a false-positive plus a true positive must equal 1. Thus the false positive rate is 1- 0.91 = .09
 

Dason

Ambassador to the humans
#4
I disagree. The .91 from the problem is P(Test positive | drug user). The question is asking for P(not a drug user | Test positive). Your reply makes it seem like you're arguing that P(A|B) = P(B|A) which is not true in general.
 

hlsmith

Not a robit
#5
Bayes' rule problems are notoriously tricky - at least for me. I found it easiest to construct the classification table using a made up sample size of around 1,000 and work from there.
 
#6
I disagree. The .91 from the problem is P(Test positive | drug user). The question is asking for P(not a drug user | Test positive). Your reply makes it seem like you're arguing that P(A|B) = P(B|A) which is not true in general.
I am arguing that P(A|B) = 1 - P(A'|B) ; A being a positive testing. B being the person is a drug user.

Also, this is one of the most poorly written test questions I've ever seen. We are all interpreting it differently.
 
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Dason

Ambassador to the humans
#7
The question gives us:
P(positive test | drug user) = 0.91
P(positive test | not a drug user) = 0.01
P(drug user) = 0.10

The question asks for: P(not a drug user | positive test).

I was saying that it seemed you were implying the answer is .09 because 1-0.91 = 1-P(positive test | drug user) = P(negative test | drug user).

This logic is flawed because P(negative test | drug user) doesn't equal P(not drug user | positive test) at least in general.

It turns out it gives the right answer because the way the numbers work out.

P(drug user | positive test) = P(positive test|drug user)*P(drug user)/(P(positive test|drug user)*P(drug user) + P(positive test | not drug user)*P(not drug user)) = (.91 * .10) / ((.91*.10 + .01*.9)) = 0.91.

Now you can use that 0.91 to say P(not drug user | positive test) =0.09
So we get the same answer but this time we did it properly.
 
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