Find some conditional probabilities. Choose a point at random in the square with sides 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. This means that the probability that the point falls in any region within the square is the area of that region. Let X be the x coordinate and Y the y coordinate of the point chosen. Find the conditional probability P(Y < 1/2 | Y > X).

(Hint: Sketch the square and the events Y < 1/2 and Y > X.)