John and George are set to meet each other at 12 o'clock. John's time of arrival, J, is distributed uniformly between 12:00 and 12:15. John will wait for George for 15 minutes. If he doesn't show up, he leaves. George's time of arrival, G, is also uniformly distributed, between 12:05 and 12:20. But he will only wait 5 minutes for John.
Find the probability of an encounter.
The Attempt at a Solution
I'm at complete lost with this problem. I think that what I have to do is find the jount probability distribution of J and G, but I couldn't say why. And the "waits for 15 minutes" thing also confuses me.