Question

Assume that there is a 55​% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk​ drive, what is the probability that during a​ year, you can avoid catastrophe with at least one working​ drive? b. If copies of all your computer data are stored on threethree independent hard disk​ drives, what is the probability that during a​ year, you can avoid catastrophe with at least one working​ drive? a. With two hard disk​ drives, the probability that catastrophe can be avoided is nothing. ​(Round to four decimal places as​ needed.) b. With threethree hard disk​ drives, the probability that catastrophe can be avoided is nothing. ​(Round to six decimal places as​ needed.)

Answer 1

a. 0.6975

b. 0.833625

Explanation:

a. The probability of both drives failing is 0.55² = 0.3025, so the probability that both drives won't fail is 1 -0.3025 = 0.6975.

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b. The probability of all three drives failing is 0.55³ = 0.166375, so the probability that all three drives won't fail is 1 -0.166375 = 0.833625.