Question

Approximately 2.2% of the Indian population is HIV positive. A test detects the HIV virus 96% of the time when it is actually present, but it returns a false positive 4% of the time when the HIV virus is not present.

If a person selected at random from India tests positive for the virus, what is the probability that this person is actually infected?

Answer 1

Answer:

2.2

Explanation:

Answer 2

Answer:

Probability that this person is actually infected from a random test is 0.35 approximately.

Explanation:

P(E) = Probability that the person selected has HIV = 2.2% = 0.022

P(G/E) = Probability that the test shows HIV+ when actually present= 96%

           = 0.96

P(F) = Probability that the person selected does not have HIV = 1 - P(E)

       = 1 - 0.022 = 0.978

P(G/F) = Probability that the test shows HIV when the person does not have  

          = 4% = 0.04

P (E/G) = $\frac{0.022 X 0.96}{0.022 X 0.96 + 0.978 X 0.04}$

          = 0.02112 / 0.06024

          = 0.35 (approx)