The number X of new cases of food poisoning reported in a random month in a cafeteria has a Poisson distribution with mean 0.5. The cafeteria is required by law to request a state inspection of its kitchen whenever 2 or more cases of food poisoning occur in a month.
a) What is the probability that the cafeteria will have to request an inspection this month?
b) The number of new cases of food poisoning in any given month is independent of the number of cases of food poisoning in all other months of the year. Let Z be the number of months (out of a twelve month year) that the cafeteria must be inspected by the state. Find the probability that the cafeteria will be inspected more than once in a year.