Question

To cross a single lane of moving traffic, we require at least five minutes of no cars. Successive car interarrival
times are independently and exponentially distributed with mean of 3 minutes. If an interval between
successive cars is longer than 5, we say that the interval represents a single opportunity to cross the lane.
Assume that car lengths are small relative to inter-car spacing and that our experiment begins the instant after
the zeroth car goes by. Determine the probability that:
a) We can cross the first time just before the 5th car goes by.
b) We shall have had exactly 6 opportunities by the instant the 20th car goes by

Answer 1