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 is a set containing n elements. A subset P of A is chosen at random. The set A is reconstructed by replacing the elements of P. A subset Q is again chosen at random. The Probability that P cap Q contain just one element, is

A is a set containing n elements. A subset P of A is chosen at random and the set A is reconstructed by replacing the random. Find the probability that Pcup Q contains exactly r elements with 1 le r le n .

A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, the probability that is rusted or is a nail 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 4 tickets numbered 00, 01, 10 and 11. Four tickets are chosen at random with replacement, the probability that the sum of numbers on the tickets is 22 is