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 $0\mathrm{.}4099.$ 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 does not exceed five years is $0\mathrm{.}8803.$ Now,

$0\mathrm{.}2668$ of the products from a manufacturer are used

for backup, while the remaining manufacturer's products

are used for main storage. What is the probability that a

laser that failed before five years came from a product

used for backup?

Select one:

a$.0\mathrm{.}19609373$

b$.0\mathrm{.}23585423$

c$.0\mathrm{.}64207559$

d$.0\mathrm{.}31770268$