Question

Let A = the event of HIV positive, P(A) = 0.05, and 100 individuals are selected for the test. What is the probability of at least one HIV positive?

Answer 1

To find the probability of at least one HIV positive, we can use the complement rule. The complement of at least one HIV positive is no HIV positive, which can be calculated as 1 - P(no HIV positive).

Step-by-step explanation:

To find the probability of at least one HIV positive, we can use the complement rule. The complement of at least one HIV positive is no HIV positive, which can be calculated as 1 - P(no HIV positive). Since the probability of no HIV positive is calculated by multiplying the probabilities of not being HIV positive for each individual, we can use the formula:

P(no HIV positive) = (1 - P(A))^n

where n is the number of individuals selected. In this case, n = 100. So, the probability of at least one HIV positive is:

P(at least one HIV positive) = 1 - P(no HIV positive) = 1 - (1 - P(A))^n = 1 - (1 - 0.05)^100