Cars arrive from the northbound section of an intersection according to a Poisson process at the rate of λN cars per minute and from the eastbound section according to a Poisson process at the rate of λE cars per minute.
a. Given that there is currently no car at the intersection, what is the probability that a northbound car arrives before an eastbound car?
b. Given that there is currently no car at the intersection, what is the probability that the fourth northbound car arrives before the second eastbound car?