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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Similar Questions

In a single throw of two dice,what is the probability of getting a total of $13$?

$A$ man and his wife appear in an interview for two vacancies. The probability of the husband's selection is $1/7$ and the probability of the wife's selection is $1/5$. What is the probability that only one of them is selected?

Check whether the following probabilities $P(A) = 0.5$,$P(B) = 0.4$,and $P(A \cup B) = 0.8$ are consistently defined.

$A$ fair coin and an unbiased die are tossed. Let $A$ be the event 'head appears on the coin' and $B$ be the event '$3$ on the die'. Check whether $A$ and $B$ are independent events or not.

If two integers are chosen at random,what is the probability that their product is an even integer?

Vedclass Test Series

Exam Paper Generator

Online Exam Module