Question: Cars arrive at a toll booth according to a Poisson process at a rate of 3 arrivals per minute.
a) What is the probability that the third car arrives within three minutes of the first car?
b) Of the cars arriving at the both, it is known that over the long run 60% are Japanese imports. What is the probability that in a given ten-minute interval 15 cars arrive at the booth, and 10 of these are Japanese imports? State your assumptions clearly.