Let X be a set containing 10 elements and P(X | vedclass

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

Question

(D) The total number of elements in the power set $P(X)$ is $2^{10}$.Since $A$ and $B$ are chosen with replacement,the total number of ways to choose

Vedclass · Accepted Answer

$\frac{^{20}C_{10}}{2^{20}}$

Vedclass · Answer

(D) The total number of elements in the power set $P(X)$ is $2^{10}$.Since $A$ and $B$ are chosen with replacement,the total number of ways to choose the pair $(A, B)$ is $(2^{10}) 	imes (2^{10}) = 2^{20}$.Let $n(A) = k$ and $n(B) = k$,where $k$ can range from $0$ to $10$.The number of ways to choose a subset with $k$ elements from a set of $10$ elements is $^{10}C_k$.Thus,the number of ways to choose $A$ and $B$ such that $n(A) = n(B) = k$ is $(^{10}C_k) 	imes (^{10}C_k) = (^{10}C_k)^2$.The total number of favorable outcomes is $\sum_{k=0}^{10} (^{10}C_k)^2$.Using the identity $\sum_{k=0}^{n} (^{n}C_k)^2 = ^{2n}C_n$,we get $\sum_{k=0}^{10} (^{10}C_k)^2 = ^{20}C_{10}$.Therefore,the required probability is $\frac{^{20}C_{10}}{2^{20}}$.

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 an equal number of elements is:

Similar Questions

$3$ balls are drawn one after the other without replacement from an urn containing $4$ red,$5$ blue and $6$ yellow balls. The probability of getting three different coloured balls is

If $4$-digit numbers greater than $5,000$ are randomly formed from the digits $0, 1, 3, 5,$ and $7$,what is the probability of forming a number divisible by $5$ when the digits are repeated?

Seven chits are numbered $1$ to $7$. Three are drawn one by one with replacement. The probability that the least number on any selected chit is $5$ is:

Six cards are drawn simultaneously from a pack of playing cards. What is the probability that $3$ will be red and $3$ will be black?

Three numbers are chosen at random from numbers $1$ to $20$. The probability that they are consecutive is

Vedclass Test Series

Exam Paper Generator

Online Exam Module