The number of accidents that a person has in a given year is a Poisson random variable with mean $\lambda$. However, we may suppose that the rate $\lambda$ depends on the person or portion of the population. Suppose that $\lambda = 2$ for 65 percent of the population, and $\lambda = 3$ for the other 35 percent.

(a) If a person is chosen at random, what is the probability that s/he will have zero accidents in a certain year?
$P(\mbox{no accidents}) =$

(b) If a person is chosen at random, what is the probability that s/he will have 2 accidents in a certain year?
$P(\mbox{2 accidents}) =$

(c) What is the conditional probability that the person will have 2 accidents in a given year, given that s/he had none in the preceding year?
$P(\mbox{2 accidents|none preceding}) =$