Solve each of the following probability problems. Show your work. 

(a) There are three banks in a country. The probability that an individual bank will fail within the next year is 0.05. What is the probability that there are zero bank failures within a year in this country? Assume that each bank failure is an independent event.
(b) You decide to randomly challenge Chads to a chess game. The probability that you win any particular chess game is 0.1. Assuming a geometric distribution, what is your average number of losses before a win?
(c) Suppose that 5% of the population has COVID-19, and there is a PCR test which is 95% accurate. What is the probability of a person testing positive if she truly has COVID-19?

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