An automobile manufacturer is concerned about a fault in the braking mechanism of a particular model. The fault can, on rare occasions, cause a catastrophe at high speed. The distribution of the number of cars per year that will experience the catastrophe is a Poisson random variable with λ = 5.
(a) What is the probability that at most 3 cars per year will experience a catastrophe?
(b) What is the probability that more than 1 car per year will experience a catastrophe?