1. Suppose that 25% of the people in a certain population carry the KBM gene. Ge

Question

1. Suppose that 25% of the people in a certain population carry the KBM gene. Geneticists have devised a test that is 90% successful in detecting the gene (that is, 90% of people who have the gene will test positive); however, the test gives a false positive rate of 20% (that is, 20% of people who don't have the gene will also test positive).

If a randomly-selected member of the population takes this test, what is the probability that they test positive?

What is the probability that someone who has tested positive actually has the KBM gene?

(Hint: we can divide the population into four categories based on whether they have the gene and whether they test positive for it.)

Explanation / Answer

The probability that someone who has tested positive actually has the KBM gene

law of total probability

P[have gene & + ] = 25% *90% = 22.5%
P[don't have gene & test +] = 75% *20% = 15%
P[test +] = 22.5 + 15 = 37.5% or 3/8

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