Bag A contains 4 green and 3 red balls and ba | vedclass

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

Question

(C) This problem is solved using Bayes' theorem.Let $E_1$ be the event of selecting bag $A$ and $E_2$ be the event of selecting bag $B$.Since one bag

Vedclass · Accepted Answer

$\frac{3}{7}$

Vedclass · Answer

(C) This problem is solved using Bayes' theorem.Let $E_1$ be the event of selecting bag $A$ and $E_2$ be the event of selecting bag $B$.Since one bag is selected at random,$P(E_1) = \frac{1}{2}$ and $P(E_2) = \frac{1}{2}$.Let $G$ be the event of drawing a green ball.Probability of drawing a green ball from bag $A$: $P(G|E_1) = \frac{4}{7}$.Probability of drawing a green ball from bag $B$: $P(G|E_2) = \frac{3}{7}$.We need to find the probability that the ball came from bag $B$ given that it is green,i.e.,$P(E_2|G)$.Using Bayes' theorem:$P(E_2|G) = \frac{P(E_2) \cdot P(G|E_2)}{P(E_1) \cdot P(G|E_1) + P(E_2) \cdot P(G|E_2)}$$P(E_2|G) = \frac{\frac{1}{2} 	imes \frac{3}{7}}{(\frac{1}{2} 	imes \frac{4}{7}) + (\frac{1}{2} 	imes \frac{3}{7})}$$P(E_2|G) = \frac{\frac{3}{14}}{\frac{4}{14} + \frac{3}{14}} = \frac{\frac{3}{14}}{\frac{7}{14}} = \frac{3}{7}$.

Bag $A$ contains $4$ green and $3$ red balls and bag $B$ contains $4$ red and $3$ green balls. One bag is selected at random and a ball is drawn,which is found to be green. What is the probability that it came from bag $B$?

Similar Questions

$A$ man speaks truth in $80 \%$ of the cases and another in $90 \%$ of the cases. While stating the same fact,what is the probability that they contradict each other?

$A$ bag contains $4$ white and $3$ red balls. Two draws of one ball each are made without replacement. Then the probability that both the balls are red is (in $/7$)

Find the probability that in a random arrangement of the letters of the word $DAUGHTER$,the letter $D$ occupies the first place.

Out of $13$ applicants for a job,there are $5$ women and $8$ men. It is desired to select $2$ persons for the job. The probability that at least one of the selected persons will be a woman is

If $A$ and $B$ are two events such that $P(A) = \frac{3}{8}$,$P(B) = \frac{5}{8}$ and $P(A \cup B) = \frac{3}{4}$,then $P(A|B) = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module