Probability that two randomly selected subsets of set {1,2,3,4,5} have exactly two elements in their

English

Gujarati

Hindi

14.Probability

medium

The probability that two randomly selected subsets of the set $\{1,2,3,4,5\}$ have exactly two elements in their intersection, is :

A

$\frac{65}{2^{7}}$

B

$\frac{65}{2^{8}}$

C

$\frac{135}{2^{9}}$

D

$\frac{35}{2^{7}}$

(JEE MAIN-2021)

Solution

Total subsets $=2^{5}=32$

Probability $=\frac{{ }^{5} C _{2} \times 3^{3}}{32 \times 32}=\frac{10 \times 27}{12^{10}}=\frac{135}{2^{9}}$

Standard 11

Mathematics

Share

Similar Questions

A committee of two persons is selected from two men and two women. What is the probability that the committee will have two men ?

easy

Out of $100$ students, two sections of $40$ and $60$ are formed. If you and your friend are among the $100$ students, what is the probability that You both enter the different sections?

easy

A committee of two persons is selected from two men and two women. What is the probability that the committee will have one man ?

easy

A three digit number is formed by using numbers $1, 2, 3$ and $4$. The probability that the number is divisible by $3$, is

medium

Two integers are selected at random from the set $\{1, 2, …, 11\}.$ Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is

hard

(JEE MAIN-2019)