You go to see the doctor about an ingrowing toenail. The doctor selects you at r

Question

You go to see the doctor about an ingrowing toenail. The doctor selects you at random to have a blood test for swine flu, (which for the purposes of this exercise we will say is currently suspected to affect 1 in 10,000 people in the USA. The test is 99% accurate, in the sense that the probability of a false positive is 1%. The probability of a false negative is zero. You test positive. What is the new probability that you have swine flu? Now imagine that you went to a friend's wedding in Mexico recently, and (for the purposes of this exercise) it is know that 1 in 200 people who visited Mexico recently come back with swine flu. Given the same test result as above, what should your revised estimate be for the probability you have the disease?

Explanation / Answer

a) P(having swine flu | tested positive) = P(having swine flu and tested positive) / P(tested positive)

= [(1/10,000)x1]/[((1/10,000)x1) + (9999/10,000)x0.01] = 0.0099

b)  P(having swine flu | tested positive) = [1x(1/200)]/[(1x(1/200)) + (199/200)x0.01]

= 0.3344

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