Solve Engineering Statistics Homework: Positive result on 2 Tests

[wolfmanzak]

Homework Statement

People in a given community who have a certain disease is 0.005. A test is available to diagnose the disease. If a person has the disease, the probability that the test will produce a positive signal is 0.98. If a person does not have the disease, the probability that the test will produce a positive signal is 0.02.

If a person tests positive on two successive tests, what is the probability that they have the disease?

Homework Equations

I was assuming statistical independence, though the problem doesn't necessarily state that, so I was contemplating just multiplying the two probabilities.

The Attempt at a Solution

I know from a previous part of the problem that the probability of having the disease, given a positive test result is .1976. I was going to multiply .1976*.1976 to get the answer for this question but according to the solution my TA provided that's wrong. His solution is .9235, which when I think about it, makes sense. But I don't know what he did to get to that value?

 

[NascentOxygen]

I know from a previous part of the problem that the probability of having the disease, given a positive test result is .1976. I was going to multiply .1976*.1976 to get the answer for this question but according to the solution my TA provided that's wrong. His solution is .9235, which when I think about it, makes sense. But I don't know what he did to get to that value?

Are you able to show the working to obtain .1976 as the answer to the earlier part? If you can do part (a) then that same method, extended to two tests, will give the answer to part (b).

http://physicsforums.bernhardtmediall.netdna-cdn.com/images/icons/icon2.gif So, work at showing how to find .1976 first.