Question

1. -/5 points details my notes ask your teacher practice another the 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) part (c) what is the probability that you must ask nineteen people? (round your answer to four decimal places.)

Explanation:

Step1: Define geometric distribution

This is a geometric distribution problem where we find the probability that the first success (finding an HIV-infected person) occurs on the 19th trial. The probability of success (infection) is $p = 0.085$, so the probability of failure is $1-p = 0.915$. The formula for the geometric distribution is $P(X=k)=(1-p)^{k-1}p$.

Step2: Substitute values into formula

Substitute $k=19$, $p=0.085$, $1-p=0.915$ into the formula:
$P(X=19)=(0.915)^{18} \times 0.085$
First calculate $(0.915)^{18}$:
$0.915^{18} \approx 0.2003$
Then multiply by 0.085:
$0.2003 \times 0.085 \approx 0.0170$

Answer:

0.0170