+274 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?
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.
