Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X), with replacement, then the probability that A and B have equal number of elements, is :

Xis a set containing10elements.Then power setP(X)contains210elements.AandBare picked at random fromP(X)with replacement.Total no. of outcomes are210.no. of ways in whichAandBhave equal no of elements is10C100C0+10C101C1+10C102C2++10C1010C10∴Probability=10C100C0+10C101C1+10C102C2++10C1010C10220=20C10220