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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 $x\epsilon A$ is :
Option: 1
$\frac{1}{2}$

Option: 2
$\frac{64}{127}$

Option: 3
$\frac{63}{128}$

Option: 4
$\frac{31}{128}$

Answers (1)

best_answer

As learnt in concept

Probability of occurrence of an event -

Let S be the sample space then the probability of occurrence of an event E is denoted by P(E) and it is defined as

$P\left ( E \right )=\frac{n\left ( E \right )}{n\left ( S \right )}$

$P\left ( E \right )\leq 1$

$P(E)=\lim_{n\rightarrow\infty}\left(\frac{r}{n} \right )$

- wherein

Where n repeated experiment and E occurs r times.

First we find subsets of A $=2^{7}-1$

$=127$

Number of subsets of s which contain x is $2^{6}$

Prob $=\frac{2^{6}}{2^{7}-1}$

$=\frac{64}{127}$

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vinayak

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