Question: A system contains two components, A and B, connected in series, as shown in the diagram. Assume A and B function independently. For the system

A system contains two components, A and B, connected in series, as shown in the diagram.

Assume A and B function independently. For the system to function, both components must function.

a. If the probability that A fails is 0.05, and the probability that B fails is 0.03, find the probability that the system functions.

b. If both A and B have probability p of failing, what must the value of p be so that the probability that the system functions is 0.90?

c. If three components are connected in series, and each has probability p of failing, what must the value of p be so that the probability that the system functions is 0.90?

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