(A) Let $E_1, E_2, E_3$ be the events of selecting bags $X, Y, Z$ respectively. Since the bag is selected at random,$P(E_1) = P(E_2) = P(E_3) = \frac{

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

(A) Let $E_1, E_2, E_3$ be the events of selecting bags $X, Y, Z$ respectively. Since the bag is selected at random,$P(E_1) = P(E_2) = P(E_3) = \frac{1}{3}$.Let $A$ be the event of drawing a one-rupee coin.The probability of drawing a one-rupee coin from each bag is:$P(A|E_1) = \frac{5}{5+4} = \frac{5}{9}$$P(A|E_2) = \frac{4}{4+5} = \frac{4}{9}$$P(A|E_3) = \frac{3}{3+6} = \frac{3}{9}$Using Bayes' Theorem,the probability that the coin came from bag $Y$ is:$P(E_2|A) = \frac{P(E_2)P(A|E_2)}{P(E_1)P(A|E_1) + P(E_2)P(A|E_2) + P(E_3)P(A|E_3)}$$P(E_2|A) = \frac{\frac{1}{3} \times \frac{4}{9}}{\frac{1}{3} \times \frac{5}{9} + \frac{1}{3} \times \frac{4}{9} + \frac{1}{3} \times \frac{3}{9}}$$P(E_2|A) = \frac{4}{5+4+3} = \frac{4}{12} = \frac{1}{3}$

Class 12 Mathematics Probability Baye's theorem

Medium

There are three bags $X$,$Y$,and $Z$. Bag $X$ contains $5$ one-rupee coins and $4$ five-rupee coins; Bag $Y$ contains $4$ one-rupee coins and $5$ five-rupee coins; and Bag $Z$ contains $3$ one-rupee coins and $6$ five-rupee coins. $A$ bag is selected at random and a coin drawn from it at random is found to be a one-rupee coin. Then the probability that it came from bag $Y$ is:

JEE MAIN 2024 All JEE MAIN

A
$\frac{1}{3}$
B
$\frac{1}{2}$
C
$\frac{1}{4}$
D
$\frac{5}{12}$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

Probability

Subtopic

Baye's theorem

Previous Year

JEE MAIN 2024 Paper All JEE MAIN years →

$A$ bag contains $19$ unbiased coins and one coin with head on both sides. One coin is drawn at random and tossed,and a head turns up. If the probability that the drawn coin was unbiased is $\frac{m}{n}$,where $\operatorname{gcd}(m, n) = 1$,then $n^2 - m^2$ is equal to:

DifficultJEE MAIN 2025

View Solution

In a manufacturing company,three machines $A$,$B$ and $C$ respectively produce $20 \%$,$30 \%$ and $50 \%$ of the total product. The defective products from $A$,$B$ and $C$ are respectively $5 \%$,$3 \%$ and $2 \%$. If an article produced by the company is selected at random and is found to be defective,then the probability that it is produced by machine $B$ is

EasyAP EAMCET 2018

View Solution

The urns $A, B$ and $C$ contain $4$ red,$6$ black; $5$ red,$5$ black and $\lambda$ red,$4$ black balls respectively. One of the urns is selected at random and a ball is drawn. If the ball drawn is red and the probability that it is drawn from urn $C$ is $0.4$,then find the square of the length of the side of the largest equilateral triangle inscribed in the parabola $y^2 = \lambda x$ with one vertex at the vertex of the parabola.

DifficultJEE MAIN 2023

View Solution

$A$ bag $P$ contains $3$ blue and $5$ red balls. Another bag $Q$ contains $4$ blue and $6$ red balls. $A$ ball is drawn at random from one of the bags and is found to be red. The probability that it is from bag $Q$ is

EasyTS EAMCET 2018

View Solution

Meera visits only one of the two temples $A$ and $B$ in her locality. The probability that she visits temple $A$ is $\frac{2}{5}$. If she visits temple $A$,the probability that she meets her friend is $\frac{1}{3}$,whereas it is $\frac{2}{7}$ if she visits temple $B$. Meera met her friend at one of the two temples. The probability that she met her at temple $B$ is

MediumKCET 2025

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

$A$ bag contains $19$ unbiased coins and one coin with head on both sides. One coin is drawn at random and tossed,and a head turns up. If the probability that the drawn coin was unbiased is $\frac{m}{n}$,where $\operatorname{gcd}(m, n) = 1$,then $n^2 - m^2$ is equal to:

$A$ bag $P$ contains $3$ blue and $5$ red balls. Another bag $Q$ contains $4$ blue and $6$ red balls. $A$ ball is drawn at random from one of the bags and is found to be red. The probability that it is from bag $Q$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module