Assume that there is a 5 % 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 three three independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive?

Question

Lilia Murphy

Mathematics

3 February, 09:52

Assume that there is a 5 % 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 three three independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive?

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Butler · Answer 1

Probability of survival of one disk, p=1-0.05=0.95

If there are n drives, and failures are independent (e. g. mechanical wear and tear, and not a lightning strike or a current spike), then

Probability of survival = p^n

(a) for two disks, P (2) = 0.95^2=0.9025

(b) for three disks P (3) = 0.95^3 = 0.8574