Basketball players arrive at a gym according to a Poisson process with an average rate of 1 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 probability that 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?

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