JEE Main 2014 · 11 Apr · Shift 1 · Mathematics Q86

MathematicsSingle correct+4 / -1Question 86 of 90

A set S contains 7 elements. A non-empty subset A of S and an element $x$ of S are chosen at random. Then the probability that $x\in A$ is :

\dfrac12

\dfrac{64}{127}

\dfrac{63}{128}

\dfrac{31}{128}

Answer and worked solution

Official answer: B

There are $127\times7$ equally likely pairs. Each element lies in $2^6=64$ subsets, so the favourable pairs number $7\times64$ :
$P=\frac{64}{127}.$

JEE Main 2014 · 11 Apr · Shift 1, Mathematics question 86