Answer:
0.1626 = 16.26% probability that the patient actually has HIV
Explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Positive test
Event B: Has HIV.
Probability of a positive test:
0.028 of 100 - 0.6 = 99.4% = 0.994(false-positive).
1 - 0.091 = 0.901 out of 0.6% = 0.006(positive). So
Probability of a positive test and having HIV:
0.901 out of 0.006. So
What is the probability that the patient actually has HIV?
0.1626 = 16.26% probability that the patient actually has HIV