There are three bags X,Y,and Z. Bag X contain | vedclass

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

Question

(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{

Vedclass · Accepted Answer

$\frac{1}{3}$

Vedclass · Answer

(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)}$$P(E_2|A) = \frac{\frac{1}{3} 	imes \frac{4}{9}}{\frac{1}{3} 	imes \frac{5}{9} + \frac{1}{3} 	imes \frac{4}{9} + \frac{1}{3} 	imes \frac{3}{9}}$$P(E_2|A) = \frac{4}{5+4+3} = \frac{4}{12} = \frac{1}{3}$

Similar Questions

$70 \%$ of the total employees of a factory are men. Among the employees of that factory,$30 \%$ of men and $15 \%$ of women are technical assistants. If an employee chosen at random is found to be a technical assistant,then the probability that this employee is a man is

$A$ man is known to speak truth $3$ out of $4$ times. He throws a die and reports that it is a six. Find the probability that it is actually a six.

$A$ bag contains $5$ balls of unknown colours. There are equal chances that out of these five balls,there may be $0, 1, 2, 3, 4,$ or $5$ red balls. $A$ ball is taken out from the bag at random and is found to be red. The probability that it is the only red ball in the bag is

$A$ family consists of $8$ persons. If $4$ persons are chosen at random and they are found to be $2$ men and $2$ women,then the probability that there are equal number of men and women in that family is

Vedclass Test Series

Exam Paper Generator

Online Exam Module