Finding probability of uniform random variable given a condition with another random variable Suppose X and Y are independent and uniformly distributed on the unit interval (0,1). Find: $$P[Y>\frac{1}{2}\,|\,Y>1-2X]$$
How I approached it was to find the area where $Y > 1 - 2X$, and used that as my denominator. I then found the area where $Y > \frac{1}{2}$ within that area, and used that as the numerator. Upon dividing I get a value of 1/2, but apparently the answer is 7/12. Where am I going wrong with this? 

The geometry is illustrated below.

The red shaded area is your numerator, and the blue shaded area your denominator.
