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.