4. There's no such thing as an accident. Suppose that the number of accidents that a person has in a given year is a Poisson random variable with mean A. However, suppose that the value of A changes from person to person, being equal to 2 for 60 percent of the population and 3 for the other 40 percent. (a) If a person is chosen at random, what is the probability that he will have (a) 0 accidents and (b) exactly 3 accidents in a certain year? (b) What is the conditional probability that he will have 3 accidents in a given year, given that he had no accidents the preceding year? (Write out all of your steps). You'll need to answer this first: what is the probability that the random person's A value is equal to 2, given that he had no accidents the preceding year? What is the probability that the random person's A value is equal to 3, given that he had no accidents the preceding year?