Testing Twice
Only 0.01% of people have triskaidekaphobia. The Dreizehn Club has developed a test for the phobia. If you have Triskadekaphobia, the test is 99% likely to identify that you have the disease. Unfortunately, it is also 5% likely to claim you have the disease when you don’t. If you take the test twice and it twice claims you have the disease, what is the probability that you do have the disease?
The answer is 0.0377.
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1 solution
P(diseased | tested positive twice).
= 99^2 * 0.01 / (99^2 * 0.01 + 5^2 * (1 - 0.01)).
= 0.03772866