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Problems on Reliability

1. A product has four critical interacting parts. Each has a 0.007 probability of failing during its usable life.
(a.) What is the reliability of each part?
(b.) What is the reliability of the product?
2. A machine has four critical component parts. If any of these components fails, the machine cannot operate. The four component reliabilities are 0.97, 0.99, 0.92, and 0.98.
(a.) Compute the system reliability of the machine
(b) If the machine could be redesigned to allow redundancy for the part that presently has a relaibility of 0.92, what would be the new system reliability of the machine?
Probability of primary component working + [(Probability of backup component working) x (Probability of needing backup component)]

I believe the answers are 1a. 0.993, 1b. 0.972
2a. 0.8658, 2b. 0.9351

If these are right, please show the work on how you got these answers
thanks

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This posting contains solution to following two problems on reliability.

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