Trains headed for destination A arrive at the train station at $15$ -minute intervals starting at 7 a.m., whereas trains headed for destination B arrive at $15$ -minute intervals starting at 7:05 a.m.
(a) If a certain passenger arrives at the station at a time uniformly distributed between $7$ and $8$ a.m. and then gets on the first train that arrives, what proportion of time does he or she go to destination A?
(b)What if the passenger arrives at a time uniformly distributed
between $7 : 10$ and $8 : 10$ a.m.?

Question

Trains headed for destination A arrive at the train station at $15$ -minute intervals starting at 7 a.m., whereas trains headed for destination B arrive at $15$ -minute intervals starting at 7:05 a.m.
(a) If a certain passenger arrives at the station at a time uniformly distributed between $7$ and $8$ a.m. and then gets on the first train that arrives, what proportion of time does he or she go to destination A?
(b)What if the passenger arrives at a time uniformly distributed
between $7 : 10$ and $8 : 10$ a.m.?

Accepted Answer

(a) If a passenger arrives at the station at a time uniformly distributed between $7$ and $8$ a.m. and then gets on the first train that arrives, then for $\frac{2}{3}$ times he or she goes to destination A

(b) If the passenger arrives at a time uniformly distributed between $7 : 10$ and $8 : 10$ a.m., then for $\frac{2}{3}$ times he or she goes to destination A.

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Part (a) Step 1. Given information.

Part (a) Step 2. Calculate the proportion of time the passenger goes to destination A, if he or she arrives the station between 7am to 8 am.

Part (b) Step 1. Calculate the proportion of time the passenger goes to destination A, if he or she arrives the station between 7:10 a.m. to 8:10a.m.

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A First Course in Probability

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Step by Step Solution

Part (a) Step 1. Given information.

Part (a) Step 2. Calculate the proportion of time the passenger goes to destination A, if he or she arrives the station between 7am to 8 am.

Part (b) Step 1. Calculate the proportion of time the passenger goes to destination A, if he or she arrives the station between 7:10 a.m. to 8:10a.m.

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