The number of accidents that a person has in a given year is a Poisson random variable with mean $. However, suppose that the value of $ changes from person to person, being equal to 3 for 75 percent of the population and 4 for the other 25 percent. If a person is chosen at random, what is the probability that he will have (a) 0 accidents and (b) exactly 4 accidents in a certain year? What is the conditional probability that he will have 4 accidents in a given year, given that he had no accidents the preceding year?