One bag contains 3 white and 2 black balls, and another bag contains 2 white and 3 black balls. Two balls are drawn at random from the first bag and put into the second bag, and then a ball is drawn from the second bag. What is the probability that the ball drawn from the second bag is white?

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: