Question

Cars cross a certain point on the highway in accordance with a Poisson process with rate = 3 per minute. If Al runs across the highway at some random time, what is the probability that he will avoid being hit by a car if the amount of time that it takes him to cross the road is s seconds? (Assume that if a car goes by while Al is on the highway, that it will hit him.)

Answer 1

rate = 3 /minute

for s second

mean = 3/60 * s = s/20

P(N(S) = 0) = e^(-s/20)

probability that he will avoid being hit by a car if the amount of time that it takes him to cross the road is s seconds = e^(-s/20)