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 South Africa, the prevalence of HIV

is 17.3%. 

Let X = the number of people you test until you find a person infected with HIV.

What is the probability that you must test 30 people to find one with HIV? Present your result with 4 decimal places.