Chapter 9, Problem 9.2PTE

Cars cross a certain point in the highway in accordance with a Poisson process with rate $\lambda =3$ per minute. If AI runs blindly across the highway, what is the probability that he will be uninjured if the amount of time that it takes him to cross the road is s seconds? (Assume that if he is on the highway when a car passes by. then he will be injured.) Do this exercise for s = 2, 5, 10, 20.