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Consider 2 mugs the first contains 2 white and 7 black

Consider 2 mugs. THe first contains 2 white and 7 black balls, and the second contains 5 white and 6 black balls. We flip a fair coin and then draw a ball from the first mug or the second mug depending on whether the outcome was heads or tails. What is the conditional probability that the outcome of the toss was heads given that a white ball was selected? (use Bayes Rule)

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