1) (10) Suppose that a person taking a flu shot contracts an average of three colds per year and that this average increases to five colds per year for persons not taking a flu shot. Suppose further that the number of colds a person contracts in a year is a Poisson random variable. a) Find the probability of less than three colds in six months for a person who took a flu shot. b) Find the probability of less than three colds in two years for a person who didn't take a flu shot.. c) What is the expected number of colds that a person not taking a flu shot will develop in18 months? d) Suppose 70% of the population takes a flu shot. Find the probability that a randomly selected person will have less than three colds in a given year