Basketball players arrive at a gym according to a Poisson process with an average rate of1 every 4 minutes. A 3-on-3 pick-up game can start as soon as 6 players have arrived.

(a) Suppose that the gym has just opened. What is the probability that the first player arrives within 3 minutes?

(b) Suppose that 4 minutes has passed since the gym opened. What is the probabilitythat first player arrives within 3 min from now?

(c) On average how long does it take to start a game?

(d) What is the probability that it takes more than 20 minutes to start a game?