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

Question

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).

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

- I've tried 37.5 for this answer which is WRONG.

b) what is the probability that someone who has tested positive actually has the KBM gene?

- I've tried 22.5 for this answer which is WRONG.

Explanation / Answer

P( gene)=0.25 , P(no gene)=1-0.25=0.75

P(+ve | gene)=0.9

P(+ve | no gene)=0.2

P(+ve)=P(+ve | gene)*P(gene)+P(+ve | no gene)* P(no gene)= 0.9*0.25+0.2*0.75=0.375

a) answer is 0.375

b) P(gene|+ve)=P(+ve | gene)*P(gene)/P(+ve)=0.9*0.25/0.375=0.6

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