There are two boxes each containing 10 balls. In each box, a few of them are black balls and the rest are white. A ball is drawn at random from one of the boxes and found to be black. If the probability that the drawn black ball came from the second box is 15, then the number of black balls in the first box is:

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: