SOLUTION: 2.25 Rapid transit trains arrive at a given station every five minutes and depart after stopping at the station for one minute to drop off and pick up passengers. Assuming trains a

Question 1204079: 2.25 Rapid transit trains arrive at a given station every five minutes and depart after stopping at the station for one minute to drop off and pick up passengers. Assuming trains arrive every hour on the hour, what is the probability that a passenger will be able to board a train immediately if he or she arrives at the station at a random instant between 7:54 a.m. and 8:06 a.m.?
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

The interval between 7:54 and 8:06 is 12 minutes long.

With the described schedule, there are trains in the station from 7:55 to 7:56, from 8:00 to 8:01, and from 8:05 to 8:06. So in the 12-minute interval from 7:54 to 8:06, there are trains in the station for 3 minutes.

The probability that there is a train in the station at any instant between 7:54 and 8:06 is then 3/12 = 1/4.

ANSWER: 1/4 or 25%

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