(C) Let $E_1, E_2, E_3$ be the events that the refrigerator is from companies $C_1, C_2, C_3$ respectively. Let $D$ be the event that the refrigerator

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

(C) Let $E_1, E_2, E_3$ be the events that the refrigerator is from companies $C_1, C_2, C_3$ respectively. Let $D$ be the event that the refrigerator is defective.Given probabilities are:$P(E_1) = 0.25, P(E_2) = 0.35, P(E_3) = 0.40$$P(D|E_1) = 0.03, P(D|E_2) = 0.02, P(D|E_3) = 0.01$Using Bayes' Theorem,the probability that the defective refrigerator is from $C_2$ is:$P(E_2|D) = \frac{P(E_2) \cdot P(D|E_2)}{P(E_1) \cdot P(D|E_1) + P(E_2) \cdot P(D|E_2) + P(E_3) \cdot P(D|E_3)}$$P(E_2|D) = \frac{0.35 \times 0.02}{(0.25 \times 0.03) + (0.35 \times 0.02) + (0.40 \times 0.01)}$$P(E_2|D) = \frac{0.0070}{0.0075 + 0.0070 + 0.0040} = \frac{0.0070}{0.0185}$$P(E_2|D) = \frac{70}{185} = \frac{14}{37}$

Class 12 Mathematics Probability Baye's theorem

Difficult

$A$ dealer gets refrigerators from $3$ different manufacturing companies $C_1, C_2$ and $C_3$. $25 \%$ of his stock is from $C_1, 35 \%$ from $C_2$ and $40 \%$ from $C_3$. The percentages of receiving defective refrigerators from $C_1, C_2$ and $C_3$ are $3 \%, 2 \%$ and $1 \%$ respectively. If a refrigerator sold at random is found to be defective by a customer,then the probability that it is from $C_2$ is

TS EAMCET 2024 All TS EAMCET

A
$\frac{29}{37}$
B
$\frac{8}{37}$
C
$\frac{14}{37}$
D
$\frac{15}{37}$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

Probability

Subtopic

Baye's theorem

Previous Year

TS EAMCET 2024 Paper All TS EAMCET years →

$A$ man speaks truth $2$ out of $3$ times. He picks one of the natural numbers in the set $S=\{1, 2, 3, 4, 5, 6, 7\}$ and reports that it is even. The probability that it is actually even is

EasyKCET 2019

View Solution

Bag $A$ contains $3$ white and $7$ red balls,and bag $B$ contains $3$ white and $2$ red balls. One bag is selected at random and a ball is drawn from it. What is the probability that the ball was drawn from bag $A$,given that the ball drawn is white?

MediumJEE MAIN 2024

View Solution

$A$ laboratory blood test is $99 \%$ effective in detecting a certain disease when it is in fact,present. However,the test also yields a false positive result for $0.5 \%$ of the healthy persons tested (that is,if a healthy person is tested,then,with probability $0.005,$ the test will imply he has the disease). If $0.1 \%$ of the population actually has the disease,what is the probability that a person has the disease given that his test result is positive?

Difficult

View Solution

Bag $I$ contains $3$ red,$4$ black,and $3$ white balls. Bag $II$ contains $2$ red,$5$ black,and $2$ white balls. One ball is transferred from Bag $I$ to Bag $II$,and then a ball is drawn from Bag $II$. The ball drawn is found to be black. What is the probability that the transferred ball was red?

MediumJEE MAIN 2022

View Solution

$A$ bag contains $2n+1$ coins. It is known that $n$ of these coins have a head on both sides,whereas the remaining $n+1$ coins are fair. $A$ coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is $\frac{31}{42}$,then $n$ is equal to

EasyTS EAMCET 2013

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

$A$ man speaks truth $2$ out of $3$ times. He picks one of the natural numbers in the set $S=\{1, 2, 3, 4, 5, 6, 7\}$ and reports that it is even. The probability that it is actually even is

Bag $A$ contains $3$ white and $7$ red balls,and bag $B$ contains $3$ white and $2$ red balls. One bag is selected at random and a ball is drawn from it. What is the probability that the ball was drawn from bag $A$,given that the ball drawn is white?

Bag $I$ contains $3$ red,$4$ black,and $3$ white balls. Bag $II$ contains $2$ red,$5$ black,and $2$ white balls. One ball is transferred from Bag $I$ to Bag $II$,and then a ball is drawn from Bag $II$. The ball drawn is found to be black. What is the probability that the transferred ball was red?

$A$ bag contains $2n+1$ coins. It is known that $n$ of these coins have a head on both sides,whereas the remaining $n+1$ coins are fair. $A$ coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is $\frac{31}{42}$,then $n$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module