(A) Let $E_1, E_2,$ and $E_3$ be the events that the items are produced by operators $A, B,$ and $C$ respectively.$P(E_1) = 50\% = 0.5, P(E_2) = 30\%

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

(A) Let $E_1, E_2,$ and $E_3$ be the events that the items are produced by operators $A, B,$ and $C$ respectively.$P(E_1) = 50\% = 0.5, P(E_2) = 30\% = 0.3, P(E_3) = 20\% = 0.2$.Let $X$ be the event that the item produced is defective.$P(X|E_1) = 1\% = 0.01, P(X|E_2) = 5\% = 0.05, P(X|E_3) = 7\% = 0.07$.We need to find $P(E_1|X)$. By Bayes' theorem:$P(E_1|X) = \frac{P(E_1)P(X|E_1)}{P(E_1)P(X|E_1) + P(E_2)P(X|E_2) + P(E_3)P(X|E_3)}$$P(E_1|X) = \frac{0.5 \times 0.01}{(0.5 \times 0.01) + (0.3 \times 0.05) + (0.2 \times 0.07)}$$P(E_1|X) = \frac{0.005}{0.005 + 0.015 + 0.014} = \frac{0.005}{0.034} = \frac{5}{34}$.

Class 12 Mathematics Probability Baye's theorem

Difficult

$A$ manufacturer has three machine operators $A$,$B$,and $C$. The first operator $A$ produces $1 \%$ defective items,whereas the other two operators $B$ and $C$ produce $5 \%$ and $7 \%$ defective items respectively. $A$ is on the job for $50 \%$ of the time,$B$ is on the job for $30 \%$ of the time,and $C$ is on the job for $20 \%$ of the time. If a defective item is produced,what is the probability that it was produced by $A$ (in $/34$)?

A
$5$
B
$15$
C
$7$
D
$1$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

Probability

Subtopic

Baye's theorem

In a college,$25\%$ of the boys and $10\%$ of the girls offer Mathematics. The girls constitute $60\%$ of the total number of students. If a student is selected at random and is found to be studying Mathematics,the probability that the student is a girl,is

Difficult

View Solution

$A$ computer producing factory has only two plants $T_1$ and $T_2$. Plant $T_1$ produces $20 \%$ and plant $T_2$ produces $80 \%$ of the total computers produced. $7 \%$ of computers produced in the factory turn out to be defective. It is known that $P(\text{defective} | T_1) = 10 P(\text{defective} | T_2)$. $A$ computer produced in the factory is randomly selected and it is not defective. Then the probability that it is produced in plant $T_2$ is

IIT 2016

View Solution

$A$ survey of people in a given region showed that $20 \%$ were smokers. The probability of death due to lung cancer given that a person smoked was $10$ times the probability of death due to lung cancer, given that a person did not smoke. If the probability of death due to lung cancer in the region is $0.006$, what is the probability of death due to lung cancer given that a person is a smoker?

MediumWBJEE 2015

View Solution

Bag $A$ contains $2$ white and $3$ red balls. Bag $B$ contains $4$ white and $5$ red balls. One bag is chosen at random and a ball is drawn from it,which is found to be red. Find the probability that it was drawn from bag $B$.

Medium

View Solution

In an entrance test, there are multiple-choice questions. Each question has four possible answers, only one of which is correct. The probability that a student knows the answer to a question is $90\%$. If the student gets the correct answer to a question, what is the probability that they were guessing?

DifficultMHT CET 2026

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

Similar Questions

In a college,$25\%$ of the boys and $10\%$ of the girls offer Mathematics. The girls constitute $60\%$ of the total number of students. If a student is selected at random and is found to be studying Mathematics,the probability that the student is a girl,is

Bag $A$ contains $2$ white and $3$ red balls. Bag $B$ contains $4$ white and $5$ red balls. One bag is chosen at random and a ball is drawn from it,which is found to be red. Find the probability that it was drawn from bag $B$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module