The number of serious accidents in a manufacturing plant has (approximately) a Poisson probability distribution with a mean of two serious accidents per month. It can be shown that if x, the number of events per unit time, has a Poisson distribution with mean l, then the time between two successive events has an exponential probability distribution with mean θ = 1>λ.
a. If an accident occurs today, what is the probability that the next serious accident will not occur within the next month?
b. What is the probability that more than one serious accident will occur within the next month?