Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random

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14.Probability

hard

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

$\frac{{\left( {{2^{10}} - 1} \right)}}{{{2^{10}}}}$

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

$\frac{{\left( {{2^{10}} - 1} \right)}}{{{2^{20}}}}$

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

(JEE MAIN-2015)

Solution

Required porbability is

$\frac{{{{\left( {^{10}{C_0}} \right)}^2} + {{\left( {^{10}{C_1}} \right)}^2} + {{\left( {^{10}{C_2}} \right)}^2} + …… + {{\left( {^{10}{C_{10}}} \right)}^2}}}{{{2^{10}}}}$

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

Standard 11

Mathematics

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(IIT-2017)

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

Solution

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