For the next two questions consider a medical test with a false positive rate of
ID: 3249809 • Letter: F
Question
For the next two questions consider a medical test with a false positive rate of 3% and a false negative rate of 2%. The frequency of the condition in people who take this test is 1% What value is closest to the percentage of people who test "positive" who are genuinely positive for the condition? (A) 25% (B) 35% (C) 45% (D) 55% (E) 65% What value is closest to the percentage of people who test "negative" who are genuinely negative for the condition? (A) 99.95% (B) 99.96% (C) 99.97% (D) 99.98% (E) 99.99%Explanation / Answer
Probability of People with the condition =0.01 , People without the condition = 0.99
P(Detect/condition present) = 0.98 P( Detect/Condition absent) = 0.03
6)P(Condition present / Detect) = P(Detect/condition present) * P( Present) / [P(Detect/condition present)* P(Present)+P(Detect/condition absent)*P(absent)] = 0.01*0.98 / [0.01*0.98+0.03*0.99] = 98 /395 = 0.25
Hence, A is the correct answer.
7) Probability = 0.99*0.97 / [ 0.99*0.97 + 0.02*0.0.01] = 0.9998 = 99.98%.
Hence, D is the correct answer.