Stats question

[Philo]

I don't know if this one's been asked before...

Suppose there is a test that is used to test if someone has taken some illegal drug that 5% of the general population uses. The test is 95% accurate, by which I mean that if someone who does in fact use the drug takes the test then the test is 95% likely to come out positive, and if someone who does not use the drug takes the test then the test is 95% likely to come out negative.

Now suppose we choose someone at random from the general population and give them the test. The test comes out positive. Given these facts, what is the actual likelihood that the person uses the drug?

[west_eh]

50%

The probability that someone uses the drug and test positive is .05*.95=.0475.

The probability that someone doesn't use the drug and test positive is .95*.05=.0475.

9.5% of the population will test positive, only half will be on the drug.

[diebitter]

I like this one for the statisticians...

Say 0.1% of the population has syphilis. A test for it is 90% accurate (90% correct if the person has it, 10% false positive, and vice versa).

If a girl tests positive, what is the chance she has syphilis?


And given this, would you have unprotected sex with her?

[Darryl_P]

Consider a group of 10,000 people. Of these, 10 will have syphilis and of these 9 will test positive and 1 will test negative. Of the 9,990 people who don't have the disease, 8,991 will test negative while 999 will test positive. So of the 1,008 people who test positive, 9 will have syphilis; therefore the sought probability is 9/1008 or 0.89%

If the girl is at least an 8 on the usual scale or a 1 on the beer scale, then yes I'd do her unprotected. I might add that her probability of being an 8 is a bit lower than usual if she was dumb enough to take such a useless test voluntarily. Subtract another point or add another beer if I have to explain stuff to her to calm her fears. Call the whole thing off if she insists on talking to some idiot doctor who is clueless about statistics before she forms an opinion about the results.