Let X be a set containing n elements. Two subsets A and B of X are chosen at random, the probability that `AuuB=X` is

Let X be a set containing n elements. If two subsets A and B of X are picked at random, the probability that A and B have the same number of elements is

A set contain n elements, then power set contains:

Let A be a finite set containing n distinct elements. The number of functions that can defined from A to A is

A is a set containing n elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P. A subset Q of A is again chosen, the number of ways of choosing so that (P cup Q) is a proper subset of A, is

A set contains 2n+1 elements. The number of subsets of this set containing more than n elements :

Two non negative integers are chosen at random. The probability that the sum of the square is divisible by 10, is

A is a set containing n elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P. A subset of A is again chosen. Find the number of ways of choosing P and Q, so that (i) P capQ contains exactly r elements. (ii) PcapQ contains exactly 2 elements. (iii) P cap Q=phi

Two positive real numbers x and y satisfying xle1 and yle1 are chosen at random. The probability that x+yle1 , given that x^2+y^2le(1)/(4) , is

A bag contains 5 red, 8 black and 7 white balls. One ball is chosen at random. What is the probability that the chosen ball is back?