Finding P[X>Y|X<2Y] for independent exponential variables

[jenuine]

Let X and Y be independent exponentially distributed random variables, each with mean 1. Find P[X>Y|X<2Y]






I know I must use conditional probability, but I can't simplify it enough to integrate.

 

[vela]

You need to show a bit more work. Keep in mind, we don't know you. None of us knows what you know and what you don't know. So even if what you've done so far seems trivial to you, you should explain what you've tried and where you're getting stuck.

For this problem, I suggest you sketch the regions of interest on the xy plane. That usually helps in seeing exactly what you need to integrate.