Uniform Distribution Probability Question

Question

Suppose trains heading for destination A arrive at the station every 15 minutes, starting at 7 A.M., while trains heading for destination B arrive at the station every 15 minutes, starting at 7:05 A.M.

Suppose also that a passenger arrives at the station at a time uniformly distributed between 7 and 8 A.M., and then adventurously hops on the first train to arrive.

What is the probability this passenger waits 5 minutes or less? Do NOT round your answer

Answer 1

The times where he has more than a 5 minute wait are for the 5 minutes after train B arrives. That is 5 minutes out of every 15 (15 goes evenly into 60 minutes) or 5/15 = 1/3 of the time. The wait being less than 5 minutes will be 1 - 1/3 = 2/3 of the time.

Please consider a tutor. Take care.