Buses headed to Longmont arrive in downtown Boulder every 30 minutes starting at 8:37am, whereas buses heading to Denver arrive 15 minutes starting at 8:31am. (a) If a passenger arrives at the station uniformly between 8:30am and 9:30am and then gets onto the first bus that arrives, what is the probability she goes to Longmont? (b) What is the passenger arrives uniformly between 8:45am and 9:45am?

(a) 20% to Longmont; 80% to Denver

(b) 20% to Longmont; 80% to Denver

Step-by-step explanation:

(a) The bus to Longmont is the first bus to arrive, only between 8:31 and 8:37, and again between 9:01 and 9:07. That is, for a total of 12 minutes every hour, the Longmont bus is the first to arrive. The probability of going to Longmont is 12/60 = 1/5 = 20%.

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(b) Same as for (a). As long as passenger arrival times are uniform within an hour, the probability is the same.