Traffic follows a Poisson process with rate 6 cars per minute. A deer runs out of the woods and tries to cross the road. If there is a car passing in the next 5 seconds then there will be a collision. (a) Find the probability of a collision. (b) What is the chance of a collision if the deer only needs 2 seconds to cross the road.
So the rate is 0.1 cars per second, and the expected number of cars in 5 seconds = 5*(6/60) = 0.5 = λ. I'm not really sure how to put this together to answer the problem.
If the average number of cars in $5$ seconds is $0.5$ then the probability of no cars during that time is $$\frac{0.5^0 e^{-0.5}}{0!}.$$