The chances of drawing a defective bulb from three factories A, B and C are 14, 15 and 16 respectively. One factory is selected at random, and a bulb is drawn from it at random. If the bulb is found to be defective, find the probability that it was produced by factory B.

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: