It is generally recognized as wise to back up computer data. Assume that there is a 11% rate of disk drive failure in a year. a. If all of a computer's data are stored on a single hard disk drive, what is the probability that the drive will fail during a year? b. If all of a computer's data are stored on a hard disk drive with a copy stored in a second hard disk drive, what is the probability that both drives will fail during a year? c. If all of a computer's data is stored on three independent hard disk drives, what is the probability that all three will fail during a year?

b. If all of a computer's data are stored on a hard disk drive with a copy stored in a second hard disk drive, what is the probability that both drives will fail during a year?

Solution:

- The given probability of one disk failing in a year does not affect the probability of another disc failing. Hence, the two events are independent.

- Hence. the probability of independent events can be calculated as:

P ( 1st disc & 2nd disc fails / year) = P(disc fail/year)*P(disc fail/year)

P ( 1st disc & 2nd disc fails / year) = 0.11*0.11 = 0.0121

c. If all of a computer's data is stored on three independent hard disk drives, what is the probability that all three will fail during a year?

- The given probability of one disk failing in a year does not affect the probability of another disc failing. Hence, the three events are independent.

- Hence. the probability of independent events can be calculated as:

P ( 1st, 2nd & 3rd disc fails / year) = P(disc fail/year)^3

P ( 1st disc & 2nd disc fails / year) = 0.11^3 = 0.001331