The traffic on the one-way main street shown below may be satisfactorily described by a Poisson process with an average rate of arrival of 8 cars per minute. A driver (indicated by the box) on the side street is waiting to cross the main street. He will cross as soon as he finds a gap of 15 sec.
a. Determine the probability, P, that a gap will be longer than 15 sec.
b. What is the probability that the driver will cross at the fourth gap? (Note that this implies that the first three gaps are too short for the driver to cross).
c. Determine the mean number of gaps he has to wait until crossing the main street.
d. What is the probability that he will cross within the first four gaps?