Question

• / 5 pointsthe world bank records the prevalence of hiv in countries around the world. according to their data, \prevalence of hiv refers to the percentage of people ages 15 to 49 who are infected with hiv.\ in one country, the prevalence of hiv is 18.5%. let x = the number of people you test until you find a person infected with hiv.part (a)part (b)what is the probability that you must test 33 people to find one with hiv? (round your answer to four decimal places.)part (c)part (d)

Explanation:

Step1: Define success probability

The probability of finding an infected person (success) is $p = 0.185$. The probability of a non-infected person (failure) is $1-p = 1-0.185 = 0.815$.

Step2: Interpret the event

Testing 33 people to find an infected one means the first 32 people are non-infected. This follows a geometric distribution, where we calculate the probability of 32 failures first.

Step3: Calculate the probability

The probability is $(1-p)^{32}$. Substitute values:
$$(0.815)^{32}$$
Calculating this gives approximately $0.815^{32} \approx 0.0012$.

Answer:

0.0012