(C) Let $n(M)$ be the number of members proficient in Mathematics and $n(S)$ be the number of members proficient in Statistics.Given $n(M \cup S) = 25

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

(C) Let $n(M)$ be the number of members proficient in Mathematics and $n(S)$ be the number of members proficient in Statistics.Given $n(M \cup S) = 25$,$n(M) = 19$,and $n(S) = 16$.Using the formula $n(M \cup S) = n(M) + n(S) - n(M \cap S)$:$25 = 19 + 16 - n(M \cap S)$$25 = 35 - n(M \cap S)$$n(M \cap S) = 35 - 25 = 10$.The probability that a person selected at random is proficient in both is $P(M \cap S) = \frac{n(M \cap S)}{n(M \cup S)} = \frac{10}{25} = \frac{2}{5}$.

Class 11 Mathematics Sets Word Problem - Set Theory

Easy

In a committee of $25$ members,each member is proficient either in Mathematics or in Statistics or in both. If $19$ of them are proficient in Mathematics and $16$ of them are proficient in Statistics,then the probability that a person selected at random from the committee is proficient in both is

AP EAMCET 2023 All AP EAMCET

A
$\frac{1}{5}$
B
$\frac{3}{5}$
C
$\frac{2}{5}$
D
$\frac{1}{2}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Sets

Subtopic

Word Problem - Set Theory

Previous Year

AP EAMCET 2023 Paper All AP EAMCET years →

Let $A = \{a_1, a_2, a_3, \dots, a_n\}$ be a set containing $n$ elements. Two subsets $P$ and $Q$ of $A$ are formed independently. The number of ways in which these subsets can be formed such that $(P - Q)$ contains exactly $2$ elements is:

View Solution

Let $X$ be the set consisting of the first $2018$ terms of the arithmetic progression $1, 6, 11, \dots$ and $Y$ be the set consisting of the first $2018$ terms of the arithmetic progression $9, 16, 23, \dots$. Then,the number of elements in the set $X \cup Y$ is:

MediumIIT 2018

View Solution

Let $S = \{1, 2, 3, \ldots, 40\}$ and let $A$ be a subset of $S$ such that no two elements in $A$ have their sum divisible by $5$. What is the maximum number of elements possible in $A$?

DifficultKVPY 2012

View Solution

In a certain town, $60 \%$ of the families own a car, $30 \%$ own a house and $20 \%$ own both a car and a house. If a family is randomly chosen, what is the probability that this family owns a car or a house but not both?

EasyWBJEE 2015

View Solution

In a survey of $400$ students in a school,$100$ were listed as taking apple juice,$150$ as taking orange juice and $75$ were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice.

Easy

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

In a committee of $25$ members,each member is proficient either in Mathematics or in Statistics or in both. If $19$ of them are proficient in Mathematics and $16$ of them are proficient in Statistics,then the probability that a person selected at random from the committee is proficient in both is

Similar Questions

Let $A = \{a_1, a_2, a_3, \dots, a_n\}$ be a set containing $n$ elements. Two subsets $P$ and $Q$ of $A$ are formed independently. The number of ways in which these subsets can be formed such that $(P - Q)$ contains exactly $2$ elements is:

Let $X$ be the set consisting of the first $2018$ terms of the arithmetic progression $1, 6, 11, \dots$ and $Y$ be the set consisting of the first $2018$ terms of the arithmetic progression $9, 16, 23, \dots$. Then,the number of elements in the set $X \cup Y$ is:

Let $S = \{1, 2, 3, \ldots, 40\}$ and let $A$ be a subset of $S$ such that no two elements in $A$ have their sum divisible by $5$. What is the maximum number of elements possible in $A$?

In a certain town, $60 \%$ of the families own a car, $30 \%$ own a house and $20 \%$ own both a car and a house. If a family is randomly chosen, what is the probability that this family owns a car or a house but not both?

In a survey of $400$ students in a school,$100$ were listed as taking apple juice,$150$ as taking orange juice and $75$ were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice.

Vedclass Test Series

Exam Paper Generator

Online Exam Module