Sam the Vet is running a rabies vaccination clinic for dogs at the local grade school

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Sam the Vet is running a rabies vaccination clinic for dogs at the local grade school. Sam can vaccinate a dog every 3 minutes. It is estimated that the dogs will arrive independently and randomly throughout the day at a rate of 1 dog every 6 minutes, according to a Poisson distribution. Also assume that Sam's vaccinating times are exponentially distributed. Find the:
(a) probability that Sam is idle.                           
(b) proportion of time that Sam is busy.                       
(c) average number of dogs receiving or waiting to be vaccinated.