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### #1

Posted 05 March 2008 - 08:08 PM

### #2

Posted 05 March 2008 - 08:22 PM

Assume that 1% of the members of a particular sports league use a particular proscribed drug. It is decided to test all of the members of the league to find these villains out. The test used has a only a 1% chance of failing to identify an actual drug user and also has only a 1% chance of misidentifying a non-drug user as a drug user. Tom tests positive -- what are the chances that, despite the results of this highly accurate drug test, he is innocent.

### #3

Posted 05 March 2008 - 08:31 PM

### #4

Posted 05 March 2008 - 08:32 PM

**Edited by GIJeff, 05 March 2008 - 08:33 PM.**

### #5

Posted 05 March 2008 - 09:17 PM

My probability and statistics teacher would kill me if he saw my post above...Spoiler for My two cents

Heck, I might've messed up again, but I always thought it was pretty cool how 1% chance of bad results can really screw the pooch on the reliability of the whole test.

And remember, people, that there is a 99% chance going in that he was innocent.

**Edited by toddpeak, 05 March 2008 - 09:23 PM.**

### #6

Posted 05 March 2008 - 09:29 PM

Assume that 1% of the members of a particular sports league use a particular proscribed drug. It is decided to test all of the members of the league to find these villains out. The test used has a only a 1% chance of failing to identify an actual drug user and also has only a 1% chance of misidentifying a non-drug user as a drug user. Tom tests positive -- what are the chances that, despite the results of this highly accurate drug test, he is innocent.

Lets see how rusty my Bayesian reasoning is....

### #7

Posted 05 March 2008 - 09:43 PM

EventHorizon has it right. A less notation based version of the answer, for those without probability training and for those who have forgotten it:

### #8

Posted 05 March 2008 - 10:15 PM

Very close toddpeak (P(A & B) = .99% not 1%; its P(A|B) that's 1%).

EventHorizon has it right. A less notation based version of the answer, for those without probability training and for those who have forgotten it:Spoiler for The Answer

Dang, I knew I missed a step. I needed to calculate P(A and B) from P(A|B). What a shame...

### #9

Posted 05 March 2008 - 10:32 PM

I love probabilityAssume that 1% of the members of a particular sports league use a particular proscribed drug. It is decided to test all of the members of the league to find these villains out. The test used has a only a 1% chance of failing to identify an actual drug user and also has only a 1% chance of misidentifying a non-drug user as a drug user. Tom tests positive -- what are the chances that, despite the results of this highly accurate drug test, he is innocent.

### #10

Posted 05 March 2008 - 11:05 PM

**retest**all the positives.

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

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