Lizzie needs to catch a train. The train arrives randomly some time between 2:00 and 3:00, waits for 20 minutes, and then leaves. If Lizzie also arrives randomly between 2:00 and 3:00, what is the probability that the train will be there when Lizzie arrives?
Since the train arrives randomly between 2:00 and 3:00 BUT WAITS FOR 20 MINUTES and then leaves. But when Lizzie also arrives randomly, she could luck out and arrive at that 20-minute window that the train is waiting. This means that Lizzie has 20 minutes out of 60 minutes, or 20 / 60 =1/3 probability that the train will be there when she arrives.