Question: There are five components. The components act independently, with component i working with probability pi, i = 1, 2, 3, 4, 5. These components form

There are five components. The components act independently, with component i working with probability pi, i = 1, 2, 3, 4, 5. These components form a system as shown in Fig. 3.7.

The system is said to work if a signal originating at the left end of the diagram can reach the right end, where it can pass through a component only if that component is working. (For instance, if components 1 and 4 both work, then the system also works.) What is the probability that the system works?

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