Uniform Random variables If $X$ and $Y $are both uniform random variables on $[\ 0,1]$
How do I go about finding the $P(X>Y>c)$ for some c in $[\ 0,1]$?
hints appreciated
My idea was to find the probability of intersection of the two, but the first probability i had no solid ideas how to calculate
thanks
Edit: they are independent

I assume $X,Y$ are independent.
$P(X^2 > Y > c) = \int_c^1 P(X^2> x) dx = \int_c^1 P(X> \sqrt{x}) dx = \int_c^1 1- \sqrt{x}dx$
$= 1-c - \int_c^1 \sqrt{x}dx = 1-c - \dfrac{2x^{3/2}}{3}|_{x=c}^{x=1} = 1 - c - (\dfrac{2}{3} - \dfrac{2c^{3/2}}{3}) = \dfrac{1}{3} - c +  \dfrac{2c^{3/2}}{3}.$
In the first inequality I condition on the value of $Y \in (c,1)$.
