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 elements, is
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 elements, is
- [JEE MAIN 2015]
- A
$\frac{{\left( {{2^{10}} - 1} \right)}}{{{2^{10}}}}$
- B
$\frac{{^{20}{C_{10}}}}{{{2^{10}}}}$
- C
$\frac{{\left( {{2^{10}} - 1} \right)}}{{{2^{20}}}}$
- D
$\frac{{^{20}{C_{10}}}}{{{2^{20}}}}$
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- [JEE MAIN 2023]