2 Toll Toll Booth. Cars enter a toll-plaza according to a Poisson distribution with an average of 4 cars per minute. (a) Find the probability that it will take more than a minute for the next three cars to arrive. (b) The cars randomly drive into one of three toll booths, with each toll booth being equally likely. Find the probability that no cars enter toll booth-1 in the next minute. (c) Find the probability that cars enter at most one of the three toll booths in the next minute. Hint: use the Binomial distribution. (d) Suppose that cars and trucks arrive according to independent Poisson processes, with an average of 4 cars per minute, and an average of 1 truck per minute. What is the probability that 2 or more cars arrive to the toll plaza arrive before the first truck arrives?