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A fair die is rolled. If 1 or 2 turns up bag A is picked, if 3 turns up bag B is picked, if 4 or5 or 6 turns up bag C is picked. A die is rolled, a bag is picked and a ball is drawn. What is the probability that the ball drawn is red given bag A contains 4 red and 5 white balls, bag B contains 3 red and 2 white balls and bag C contains 3 red and 4 white balls? If the ball drawn found to be red then find the probability that 3 turned up on the die?

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