A product is made of two key components: Component A, which has a random failure rate of three in every twenty hours of operation; and Component B, which has a random failure rate of two in every ten hours. PLEASE SHOW YOUR WORK
1. What is the reliability of Component A? 2. What is the reliability of the Component B? 3. What is the probability that the product will perform reliably for one hour? 4. If an identical backup is added for Component B, with a switch that is 100% reliable, what is the probability that the product will perform reliably for one hour? 5. If both Components A and B have identical backups with switches that are .95 reliable, what is the reliability of the product?