Toll booth question

If the time between successive trucks arriving at a toll booth is an exponential random variable w/ parameter theta=3 find probability that theres a wait of more than 4 min between the 5th and 7th car arriving on any day.

am i to solve this using the CDF(x) = 1 - e-cx or is that the wrong approach ?


TS Contributor
It involves the sum of two independent exponential distribution which results in an Erlang (Gamma) distribution. Have you learn that yet?

Or in class they teach you something about the Poisson process instead?
We've learned about the Poisson process and just started the Gamma distribution but i think i figured out the answer using the Gamma distribution