19. (Reliability of Systems) To transfer water from point A to point B, a water-supply system with five water pumps located at the points 1, 2, 3, 4, and 5 is designed as in Figure 9.5. Suppose that whenever the system is turned on for water to flow from A to B, pump i, i ≤ 5, functions with probability pi independent of the other pumps. What is the probability that, at such a time, water reaches B?

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B 5 4 3 2 1 A