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

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.

Step-by-step 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:

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.

4.08%

step-by-step explanation:

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