A container holds some yellow, orange, and purple marbles. The probability of drawing a yellow marble is p, and the probability becomes 1.5p if half of the orange marbles are removed from the container. If one-fourth of the marbles are purple, find the value of p.

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: