The average amount of time till a car accident on a particular 60-mile stretch of road is 30 minutes. Assume (unreasonably) that car accidents are independent, and that two accidents cannot occur at the same time.
(a) What is the probability of a car accident occurring in the first hour?
(b) What is the probability of a car accident occurring between 15 and 45 minutes?
(c) What is the variance of the time until a car accident occurs?
(d) If a car accident has not happened in 2 hours, what is the probability it will happen in the next hour?