John needs to catch a train. The train arrives randomly some time between 2:00 and 3:00, waits for 15 minutes, and then leaves. If John also arrives randomly between 2:00 and 3:00, what is the probability that the train will be there when John arrives?
John has a \(100\)% chance of being there if he arrives at \(2:20\) or earlier. Add \(\frac13\).
At \(3:00\), he has a \(\frac13\) chance. We can take this and take the average from \(2:20\) and \(3:00\) to get \(\frac23\) for this \(40\) minute period. Multiply this by the portion of time. Add \(\frac49\) to the probability.
Result: He has a \(\frac79\) chance of catching the train.
Credit to helperid1839321; https://web2.0calc.com/questions/john-needs-to-catch-a-train#r1
P.S. I changed up helperid1839321's answer a little, so please give me a little credit also!