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  4. Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is draw from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is:

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Q. Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is draw from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is:

JEE MainJEE Main 2022Probability - Part 2

Solution:

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A : Drown ball from boy II is black
B : Red ball transferred
$P\left(\frac{B}{A}\right)=\frac{P(A \cap B)}{P(A)}$
$=\frac{\frac{3}{9} \times \frac{5}{10}}{\frac{3}{9} \times \frac{5}{10}+\frac{4}{9} \times \frac{6}{10}+\frac{3}{9} \times \frac{5}{10}} $
$ =\frac{15}{15+24+15}=\frac{15}{54}=\frac{5}{18}$