If the joint probability density of X and Y is by
f(x,y) = 2 for x>0, y>0, x+y<1
f(x,y) = 0 elsewhere
find P(X>2Y)
For this problem your best policy is to draw a diagram (makes a mystic symbol in the air to ward off the wrath of Bourbaki).
The joint distribution is the uniform distribution over the triangle with vertices at (0,0), (1,0) and (0,1) in the x-y plane.
So the probability you want is the area of this triangle cut off by the line y=x/2.
That is it is the area of the triangle with vertices (0,0), (1,0), (2/3, 1/3).
CB