## Welcome to BrainDen.com - Brain Teasers Forum

 Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-)
Guest Message by DevFuse

15 replies to this topic

### #1 Topher

Topher

Newbie

• Members
• 10 posts

Posted 05 March 2008 - 08:08 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.
• 0

### #2 brhan

brhan

• Members
• 466 posts

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.

Spoiler for my guess

• 0

### #3 toddpeak

toddpeak

Junior Member

• Members
• 77 posts

Posted 05 March 2008 - 08:31 PM

Spoiler for My two cents

• 0

### #4 GIJeff

GIJeff

• Members
• 108 posts

Posted 05 March 2008 - 08:32 PM

Spoiler for My take

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

• 0

### #5 toddpeak

toddpeak

Junior Member

• Members
• 77 posts

Posted 05 March 2008 - 09:17 PM

Spoiler for My two cents

My probability and statistics teacher would kill me if he saw my post above...
Spoiler for I messed up before.

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.

• 0

### #6 EventHorizon

EventHorizon

Senior Member

• VIP
• 512 posts
• Gender:Male

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....

Spoiler for yay for probabilities!

• 0

### #7 Topher

Topher

Newbie

• Members
• 10 posts

Posted 05 March 2008 - 09:43 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:

• 0

### #8 toddpeak

toddpeak

Junior Member

• Members
• 77 posts

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:

Dang, I knew I missed a step. I needed to calculate P(A and B) from P(A|B). What a shame...
• 0

### #9 statman

statman

• Members
• 124 posts

Posted 05 March 2008 - 10:32 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.

I love probability
Spoiler for probability is fun

• 0

### #10 bonanova

bonanova

bonanova

• Moderator
• 5918 posts
• Gender:Male
• Location:New York

Posted 05 March 2008 - 11:05 PM

Spoiler for Let's make it intuitive...
The league should retest all the positives.
• 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#### 0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users