In New York City, at certain subway stations where different subway lines conver

Question

In New York City, at certain subway stations where different subway lines converge, passengers routinely hover around stairways and rush upstairs to a train headed for Penn Station if it arrives first, and if not they stay on the lower platform and catch the train to Grand Central if it is the one that comes first. Trains headed for Grand Central arrive at the train station at 15 minute intervals starting at 6:00am, whereas trains headed for Penn Station arrive at the train station at 15 minute intervals starting at 6:05am.

If Jane arrives at the train station at a time uniformly distributed between 6:00am and 7:00am, and then gets on the first train that arrives, what proportion of the time does she go to Penn Station?

Explanation / Answer

she catches train which goes to Penn station if she arrve from :6:00 to 6:05; 6:15 to 6:20 ; 6:30:6:35, 6:45:6:50

whcih comrises of 20minutes out of 60, hence probabilty she catches penn station train =20/60=1/3

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