Question

48. About 0.01% of men with no known risk behavior are infected with HIV. The false negative rate for the standard HIV test 0.01% and the false positive rate is also 0.01%. If a randomly selected man with no known risk behavior tests positive for HIV, what is the probability that he is actually infected with HIV

Answer 1

Explanation:

1. 
   `.0001 *9999/ .0001* .9999+ .0001* .9999=(1)/(2) = 50%`%

Answer 2

The probability that he is actually infected with HIV given that the man selected with no known risk behavior tests positive for HIV is 0.9999.

Explanation:

Denote the events as follows:

X = a man with no known risk behavior is infected with HIV

Y = the test is positive

The information provided is:

P (X) = 0.0001

P (Y'|X) = 0.0001

P (Y'|X') = 0.0001

Compute the probability that he is actually infected with HIV given that the man selected with no known risk behavior tests positive for HIV as follows:

`P(Y|X) = 1-P(Y'|X)\\=1-0.0001\\=0.9999`

Thus, the probability that he is actually infected with HIV given that the man selected with no known risk behavior tests positive for HIV is 0.9999.