S$3$: Buses arrive at a stop via the Poisson process, and on average, $1$ bus arrives every $10$ minutes. The following

answer the questions. $($You must write down the formulas you will use when answering. Also,

You must use terminology and symbols. Write at least $4$ digits after the comma.$)$

$($a$)$ What is the probability that at most $3$ buses will arrive at the stop within $1$ hour?

$($b$)$ What is the probability that the time until the $4$th bus arrives at the stop will be longer than $1$ and a half hours?