Semiconductor lasers used in optical storage products require higher power levels for write operations than for read operations. High-power-level operations lower the useful life of the laser. Lasers in products used for backup of higher speed magnetic disks primarily write, and the probability that the useful life exceeds five years is 0.95. Lasers that are in products that are used for main storage spend approximately an equal amount of time reading and writing, and the probability that the useful life exceeds five years is 0.995. Now, 25% of the products from a manufacturer are used for backup and 75% of the products are used for main storage. Let A denote the event that a laser’s useful life exceeds five years, and let B denote the event that a laser is in a product that is used for backup. Use a tree diagram to determine the following:
(a) P (B)
(b) P (A|B)
(c) P (A|B’)
(d) P (A ∩ B)
(e) P (A ∩ B’)
(f) P (A)
(g) What is the probability that the useful life of a laser exceeds five years?
(h) What is the probability that a laser that failed before five years came from a product used for backup?