A point (X,Y) is chosen uniformly at random from the square region defined by 0 ≤ X ≤ 1 and 0 ≤ Y ≤ 1. What is the probability that the distance of the point from the origin (0,0) is less than or equal to 1/2 and the point's X-coordinate is greater than its Y-coordinate (X > Y)?

A box contains 'x + 4' red, 'x – 1' green and 'x – 5' blue balls. If two balls are drawn from the bag one after another without replacement, then the probability of getting one red and one green ball is equal to the probability of getting a sum equal to or more than 8 when two fair dice are rolled. Find the probability of drawing a red ball when one ball is drawn at random from the bag.

Four persons are chosen at random from a group containing 3 men, 2 women, and 4 children. The probability that exactly two of them are children is: