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 $0\mathrm{.}6046.$ 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 $0\mathrm{.}1271.$ Now, $0\mathrm{.}7692$ 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$.0\mathrm{.}60153772$

b$.0\mathrm{.}82629493$

c$.1\mathrm{.}60901398$

d$.0\mathrm{.}91203370$