Probability: Let X be a set containing 10 elements and P(X) be its power set. If… | JEE Main 2015

JEE Main 2015 (Online) 10th AprilQuestion 1

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 :

Probability

$\frac{2^{10}-1}{2^{20}}$$\frac{{}^{20}C_{10}}{2^{20}}$✓ Correct answer$\frac{{}^{20}C_{10}}{2^{10}}$$\frac{2^{10}-1}{2^{10}}$

Solution

Favourable pairs $=\sum_k\binom{10}k^2=\binom{20}{10}$ out of $2^{10}\cdot2^{10}$. Probability $=\frac{\binom{20}{10}}{2^{20}}$.

Probability - JEE Mathematics question (JEE Main 2015 (Online) 10th April)

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