Bag A contains 3 white and 7 red balls,and ba | vedclass

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(C) Let $E_1$ be the event that bag $A$ is selected and $E_2$ be the event that bag $B$ is selected.Let $E$ be the event that a white ball is drawn.Gi

Vedclass · Accepted Answer

$\frac{1}{3}$

Vedclass · Answer

(C) Let $E_1$ be the event that bag $A$ is selected and $E_2$ be the event that bag $B$ is selected.Let $E$ be the event that a white ball is drawn.Given that the bags are selected at random,$P(E_1) = P(E_2) = \frac{1}{2}$.The probability of drawing a white ball from bag $A$ is $P(E|E_1) = \frac{3}{3+7} = \frac{3}{10}$.The probability of drawing a white ball from bag $B$ is $P(E|E_2) = \frac{3}{3+2} = \frac{3}{5}$.Using Bayes' theorem,the probability that the ball was drawn from bag $A$ given that it is white is:$P(E_1|E) = \frac{P(E_1) \cdot P(E|E_1)}{P(E_1) \cdot P(E|E_1) + P(E_2) \cdot P(E|E_2)}$$P(E_1|E) = \frac{\frac{1}{2} 	imes \frac{3}{10}}{\frac{1}{2} 	imes \frac{3}{10} + \frac{1}{2} 	imes \frac{3}{5}}$$P(E_1|E) = \frac{\frac{3}{20}}{\frac{3}{20} + \frac{3}{10}} = \frac{\frac{3}{20}}{\frac{3+6}{20}} = \frac{3}{9} = \frac{1}{3}$.

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?

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