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Alex needs to catch a train. The train arrives randomly some time between 1:00 and 2:00, waits for 10 minutes, and then leaves. If Alex also arrives randomly between 1:00 and 2:00, what is the probability that the train will be there when Alex arrives?

 Jun 3, 2023
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The probability that Alex will catch the train is 10/60 = 1/6.

The train arrives randomly some time between 1:00 and 2:00, waits for 10 minutes, and then leaves. This means that the train will be at the station for 10 minutes out of the 60 minutes between 1:00 and 2:00.

Alex also arrives randomly between 1:00 and 2:00. This means that Alex has an equal chance of arriving at any time between 1:00 and 2:00.

Therefore, the probability that Alex will catch the train is the probability that Alex arrives during the 10 minutes that the train is at the station. This probability is 10/60 = 1/6.

 Jun 7, 2023

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