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

Question

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?

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Margaret 4 weeks 2021-12-27T09:09:52+00:00 1 Answer 0 views 0

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    2021-12-27T09:11:08+00:00

    Answer:

    a.0.11

    b. 0.0121

    c. 0.001331

    Step-by-step explanation:

    Given:

    – The probability of 1 disk fails per year = 0.11

    Find:

    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?

    Solution:

    – The probability given is given to be 0.11 for a disk to fail. If there is one hard disk then the failure of data is equivalent.

    Hence,             P ( disc fails/year) = 0.11

    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

         

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