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A learning experiment requires a rat to run a maze (a network of pathways) until it locates one of three possible exits. Exit 1 presents

A learning experiment requires a rat to run a maze (a network of pathways) until it locates one of three possible exits. Exit 1 presents a reward of food, but exits 2 and 3 do not. (If the rat eventually selects exit 1 almost every time, learning may have taken place.) Let denote the number of times exit is chosen in successive runnings. Assume that the rat chooses an exit at random on each run. Find the probability that = 3 runs result in 1 = 1, 2 = 1, and 3 = 1.

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