Bowl B1 contains 3 white and 9 red marbles; bowl B2 contains 8 white and 4 red marbles; bowl B3 contains 10 white and 2 red marbles. A card is drawn from an ordinary deck of playing cards. If a face card (*king', 'queen' or 'jack') is drawn, a marble is selected from bowl Bi; if an 'ace' is drawn, a marble is selected from bowl B2; if any other card is drawn, a marble is selected from bowl B3. (a) What is the prior probability for choosing the three bowls? (b) Compute the probability of drawing a white marble. (c) Suppose that a bowl is selected by another student in this manner and handed to you without your being told which bowl you hold. If you select a white marble from the bowl, evaluate the posterior probability of each of the three bowls being selected.

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