A set S contains 7 elements. A non-empty subs | vedclass

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(B) Let $S = \{x_1, x_2, x_3, x_4, x_5, x_6, x_7\}$.The total number of non-empty subsets of $S$ is $2^7 - 1 = 127$.Let the chosen element be $x_i$. W

Vedclass · Accepted Answer

$\frac{64}{127}$

Vedclass · Answer

(B) Let $S = \{x_1, x_2, x_3, x_4, x_5, x_6, x_7\}$.The total number of non-empty subsets of $S$ is $2^7 - 1 = 127$.Let the chosen element be $x_i$. We want to find the number of non-empty subsets $A$ such that $x_i \in A$.For any subset $A$,each of the $7$ elements can either be included or excluded,giving $2^7$ total subsets.If we fix $x_i$ to be in the subset,the remaining $6$ elements can either be included or excluded,giving $2^6 = 64$ such subsets.Since $64$ is non-zero,all these $64$ subsets are non-empty.Thus,the probability that $x \in A$ is $\frac{64}{127}$.

$A$ 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

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