A college campus has a student coffee shop, which the students normally visit during their short breaks. Arrival at a coffee shop follows a Poisson distribution

on an average at the rate of $3$ per minute. The service counter takes about $15$ seconds on an average to attend a student and the service time follows an exponential distribution. Determine the following :

$($i$)$ Probability that the server is idle.

$($ii$)$ Expected waiting time of the student at the coffee shop.