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

    $\frac{{^{20}{C_{10}}}}{{{2^{20}}}}$

Similar Questions

A fair coin is tossed $100$ times. The probability of getting tails an odd number of times is

In a certain lottery $10,000$ tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy two ticket.

Three integers are chosen at random from the first $20$ integers. The probability that their product is even, is

If $4 \,-$ digit numbers greater than $5,000$ are randomly formed from the digits $0,\,1,\,3,\,5,$ and $7,$ what is the probability of forming a number divisible by $5$ when, the digits are repeated ?

A committee has to be made of $5$ members from $6$ men and $4$ women. The probability that at least one woman is present in committee, is