A bag contains 6 black balls and some blue balls. Another bag contains 5 black and 7 blue balls. One ball is chosen at random from each bag. Let the number of blue balls in the first bag be n, and the probability that one ball is black and the other is blue be P. Consider the following pairs of (n, P): I. n = 4, P = 1733 II. n = 5, P = 1337 III. n = 6, P = 23 Which of the following statements is correct?

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: