5.106 The mean number of automobiles entering a mountain tunnel per 2-minute period is one. An excessive number of cars entering the tunnel during a brief period of time produces a hazardous situation.

a Find the probability that the number of autos n entering the tunnel during a 2-minute period exceeds three.

b Assume that the tunnel is observed during ten 2-minute intervals, thus giving 10 independent observations, Y1, Y2, …, Y10, on a Poisson random variable. Find the probability that Y  3 during at least one of the ten 2-minute intervals.