Let S be a sample space and two mutually exclusive events A and B be such that $$A\, \cup \,B = \,S$$. If P(.) denotes the probability of the event, the maximum value of P(A) P(B) is ________________.

The probability that a given positive integer lying between 1 and 100 (both inclusive) is NOT divisible by 2, 3 or 5 is _______________

Four fair six-sided dice are rolled. The probability that the sum of the results being 22 is X/1296. The value of X is__________

Suppose a fair six-sided die is rolled once. If the value on the die is 1, 2 or 3 the die is rolled a second time. What is the probability that the sum total of values that turn up is at least 6?