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Three urns contain 2 white and 3 black balls; 3 white and 2 black balls, and 4 white and 1 black ball

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Three urns contain 2 white and 3 black balls; 3 white and 2 black balls, and 4 white and 1 black ball respectively. One ball is drawn from an urn chosen at random, and it was found to be white. Find the probability that it was drawn from the first urn. Select the correct answer from above options

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let A : Ball drawn from bag A B : Ball is drawn from bag B C : Ball is drawn from bag C BB : Black ball WB : White ball Assuming, selecting bags is of equal probability i.e. \(\frac{1}{3}\) We want to find P(A|W), i.e. probability of selected White ball is from bag A Conclusion: Therefore, the probability of selected white ball is from bag A is \(\frac{2}{9}\)

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