C.Child.CARE is a walk-in pediatric clinic. Patients arrive at Child.CARE at a rate of 8 per hour according to a Poisson distribution. Currently, the clinic has three physicians who work independently. As patients arrive to Child.CARE, they wait on a single queue for the first available physician to serve them. Each physician spends, on average, 20 minutes with each patient. The service time follows a negative exponentially distribution.

a) What is the probability of all physicians being idle?(2 points)

b) What is the probability that a customer will have to wait?(2 points)