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Three children take turns shooting a ball at a basket. They each shoot until they miss...

Three children take turns shooting a ball at a basket. They each shoot until they miss and then it is the next child’s turn. Suppose that child i (1 ≤ i ≤ 3) makes a basket with probability p and that successive trials are independent. Determine the proportion of time in the long run that each child shoots. (Assume each shot takes one time unit.)

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