CMIMC 2018 Combinatorics Problem 4

At \text{CMU}, the A and the B buses arrive once every 20 and 18 minutes, respectively. Kevin prefers the A bus but doesn’t want to wait for too long, so he commits to the following waiting scheme: he’ll take the first A bus that arrives, but after waiting for five minutes he’ll take the next bus that comes, no matter what it is. Determine the probability that he ends up on an A bus.