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

$\begin{array}{1 1} \frac{^{20}C_{10}}{2^{10}} \\ \frac{(2^{10}-1)}{2^{20}} \\ \frac{(2^{10}-1)}{2^{10}} \\ \frac{^{20}C_{10}}{2^{20}}\end{array}$