As Brian is leaving for college, his parents give him a car, but warn him that they would take the car away if he gets 6 speeding tickets. Suppose that Brian receives speeding tickets according to Poisson process with the average rate of one ticket per six months.
a) Find the probability that it would take Alex longer than two years to get his sixth speeding ticket.
b) Find the probability that it would take Alex less than four years to get his sixth speeding ticket.