Question

Semiconductor lasers used in optical storage require higher power levels for write operations than for read operations. Higher power-level operations reduce the useful life of the laser. Lasers in products used for backup of high-speed magnetic disks primarily write & their probability that their useful life exceeds 5 years is 0.95. Lasers that are used for main storage spend an equal amount of time reading and writing, and the probability that the useful life exceeds 5 years is 0.995. For all lasers used in products, 25% are used for backup and 75% are used for main storage.

Let A denote

Answer 1

Let A denote the event that a laser’s useful life exceeds 5 years, and let B denote the event that a laser is in a product used for backup.

(a) Draw a Venn diagram and label Pr(B), Pr(B’), Pr(A|B), Pr(A|B’), Pr(A’B) & Pr(A’B’).
(b) Draw a tree diagram & label Pr(B), Pr(B’), Pr(A|B), Pr(A|B’), Pr(A’|B) & Pr(A’|B’).
(c) What is the probability that the life exceeds 5 years given that laser is used for backup?
(d) What is the probability that the life exceeds 5 years given that laser is used for main storage?
(e) What is the probability that the life exceeds 5 years and laser is used for backup?
(f) What is the probability that the life exceeds 5 years and laser is used for main storage?
(g) What is the probability that the laser’s useful life exceeds 5 years?
(h) What is the probability that a laser that failed before 5 years came from a product that was used for backup?

Answer 2

@ranga

Answer 3

@ybarrap

Answer 4

leave part a and b just start from part c