Consider the following two experiments: Experiment I: A pair of dice is thrown 6 times. Let P1 be the probability of getting a doublet on exactly 5 throws. Experiment II: A coin is tossed 6 times. Let P2 be the probability of getting a head on exactly 4 throws. The ratio of P1 and P2 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: