What is the expected time it takes to the ?y to escape

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Suppose you've caught a ?y in a box. The box has three small holes connected to thin pipes. The ?rst hole is connected to a pipe that returns the ?y to the box after 5 minutes. The second is connected to a pipe that takes the ?y back to the box in 12 minutes. (Assume these two pipes are "one-way" roads; the ?y cannot re-enter any pipe returning it to the box.) The third hole is connected to the outside world through a pipe that takes the ?y 8 minutes to get through. Given that the ?y constantly tries to escape, and that it chooses randomly the three holes, with probability p1 = 0.5, p2 = 0.3 and p3 = 0.2, respectively, what is the expected time it takes to the ?y to escape?

Reference no: EM132394270

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