Chose a point at random in a square with sides 0<x<1 and 0<y<1. Let X be the x coordinate and Y be the y coordinate of the point chosen. Find the conditional probability P(y<1/2 / y>x).

Well, you can do it fairly easily with the help of a sketch. On graph paper, your square will have a vertice on the origin and two vertices on the x and y axes. Have dotted lines on the lines y=1 and x=1. Then, graph the line y=1/2 and y=x. I guess your '/' in your probability means 'and'. Then, find the area below the line y=1/2, which is above the line y=x.

Below y = 1/2 because the value has to be less that 1/2.
Above y = x because the values has to be larger than x.

Put the resulting area over the area of the square to have your probability.

Well, you can do it fairly easily with the help of a sketch. On graph paper, your square will have a vertice on the origin and two vertices on the x and y axes. Have dotted lines on the lines y=1 and x=1. Then, graph the line y=1/2 and and y=x. I guess your '/' in your probability means 'and'. Then, find the area below the line y=1/2, which is above the line y=x.

Below y = 1/2 because the value has to be less that 1/2.
Above y = x because the values has to be larger than x.

Put the resulting area over the area of the square to have your probability.

Oops, now that I learned about conditional probabilities, I see that his is wrong.
The way you would solve it using the method I described would give you 1/8, but the answer is actually 1/4.

This is because:

P(y<0.5 |y>x) = \frac{P(y<0.5 \cap y>x)}{P(y>x)}

So, for anyone who'd like to solve it...