2. Screening tests for HIV have become very accurate with growing technology, but still do not have 100% accuracy, due to some detection issues of the antibodies.

Assume that one particular test has a 10% false positive rate, and a 1% false negative rate.

The false positive rate is defined as P(Test Positive| HIV Negative),

The false negative rate is defined as P(Test Negative| HIV positive).

Assume that in a certain population of interest, 5% of people currently have HIV (are HIV positive).

2a)Find the sensitivity for this test. The sensitivity should be written as a conditional probability in the context of this problem.

2b)What is the probability that a person selected at random would test positive for HIV?

In symbols, what is P(Test Positive)?