The boulevards leading into Paris appear to drivers as endless string of traffic lights, one after other, extending as far as the eye can see. Fortunately, such successive traffic lights are synchronized. Suppose that the effect of synchronization is that a driver has a 95% chance of not being stopped at any light, independent of number of green lights she has already passed. Let X be random variable which counts the number of green lights she passes before being stopped by red light.
(a) Determine the probability distribution of X?
(b) How many green lights does she pass on average before having to stop at the red light?
(c) Determine the probability that she will get through 20 lights before having to stop for the first time?
(d) Determine the probability that she will get through 50 lights before stopping for the fourth time?