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  • Bag A contains 3 red and 2 black balls, while bag B contains 2 red and 3 black balls. A ball drawn at random from bag A is transferred to bag B and then one ball is drawn at random from bag B. If this ball was found to be a red ball, find the probabili

Bag A contains 3 red and 2 black balls, while bag B contains 2 red and 3 black balls. A ball drawn at random from bag A is transferred to bag B and then one ball is drawn at random from bag B. If this ball was found to be a red ball, find the probability that the ball drawn from bag A was red.

 

 

 

 
 
 
 
 

Answers (1)

Let the events be
E1: transforming a red ball from A to B
E2: transforming a black ball from A to B
A: getting a red ball from bag B
p\left ( E_{1} \right )= \frac{3}{5},p\left ( E_{2} \right )= \frac{2}{5}
p\left ( \frac{A}{E_{1}} \right )= \frac{1}{2},p\left ( \frac{A}{E_{2}} \right )= \frac{1}{3}
p\left ( \frac{E_{1}}{A} \right )= \frac{p\left ( E_{1} \right )\cdot p\left ( \frac{A}{E_{1}} \right )}{p\left ( E_{1} \right )p\left ( \frac{A}{E_{1}} \right )+p\left ( E_{2} \right )p\left ( \frac{A}{E_{2}} \right )}
= \frac{\frac{3}{5}\cdot \frac{1}{2}}{\frac{3}{5}\cdot \frac{1}{2}+\frac{2}{5}\cdot \frac{1}{3}}= \frac{9}{13}

Posted by

Ravindra Pindel

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