How to go about solving this?

Question

Let X and Y be two independent uniform distributed random variables each on the interval (0,1). Find P( X < 2Y | X < 3Y).

Any hints would help greatly. Thanks.

Answer 1

I'm a bit rusty with Bayesian probability, but as I read this, the first "event" is to find the probability that x<3y. You can (and should) draw a picture of the problem, and will find this probabiltiy is 5/6. For the total distribution, the probability that x<2y is 3/4. Then for this probability, the result is
(3/4)/(5/6) or 9/10