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 :

Question

( A ) $\frac{(2^{10} -1)}{2^{20}}$
( B ) $\frac{^{20}C_{10}}{2^{10}}$
( C ) $\frac{^{20}C_{10}}{2^{20}}$
( D ) $\frac{(2^{10} -1)}{2^{10}}$