Semiconductor lasers used in optical storage products requirehigher power levels

Question

Semiconductor lasers used in optical storage products requirehigher 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 disksprimarily write, and the probability that the useful life exceedsfive years is 0.95. Lasers that are in products that are used formain storage spend approximately an equal amount of time readingand writing, and the probability that the useful life exceeds fiveyears is 0.995. Now, 25% of the products from a manufacturer areused for backup and 75% of the products are used for mainstorage.
Let A denote the event that a laser's useful life exceedsfive years, and let B denote the event that a laser is in a productthat 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 exceedsfive years?
(h) What is the probability that a laser that failed before fiveyears came from a product used for backup?

Explanation / Answer

b) P(AIB) =0.95

c) P(AIB') =0.995

d) P(A B) = P(AIB)P(B) = 0.95(0.25) = 0.2375

e) P(AB') =P(AIB')P(B') = 0.995(0.75) = 0.74625

f) P(A) = P(AB)+ P(AB') = 0.95(0.25) + 0.995(0.75) =0.98375

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