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Math Help - Probability chance Qn

  1. #1
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    Probability chance Qn

    A software company employs 3 programmers in one of their subsidiaries. The percentage of code written by each programmer and the percentage of errors in their code are shown in the following table:
    Programmer
    Percentage of
    Code Written
    Percentage of
    Errors in Code
    A
    55%
    2%
    B
    35%
    3%
    C
    10%
    5%

    i) Suppose a programmer is selected at random. Before the code is examined, what is the chance that it was written by:
    Programmer A?
    Programmer B?
    Programmer C?

    ii) Suppose that the code is examined and found to contain errors.
    After this examination, what is the chance that it was written by:
    Programmer A?
    Programmer B?
    Programmer C?
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  2. #2
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    Quote Originally Posted by matty888 View Post
    A software company employs 3 programmers in one of their subsidiaries. The percentage of code written by each programmer and the percentage of errors in their code are shown in the following table:
    Programmer
    Percentage of
    Code Written
    Percentage of
    Errors in Code
    A
    55%
    2%
    B
    35%
    3%
    C
    10%
    5%

    i) Suppose a programmer is selected at random. Before the code is examined, what is the chance that it was written by:
    Programmer A?
    Programmer B?
    Programmer C?

    ii) Suppose that the code is examined and found to contain errors.
    After this examination, what is the chance that it was written by:
    Programmer A?
    Programmer B?
    Programmer C?
    i) Surely you can do this!

    ii) You need the concept of conditional probability. I'll do one of them:

    Pr(A | Error) = Pr(A and Error)/Pr(Error).

    Pr(A and Error) = Pr(Error | A) Pr(A) = (0.02)(0.55) = .....

    Pr(Error) = Pr(Error | A) Pr(A) + Pr(Error | B) Pr(B) + Pr(Error | C) Pr(C) = (0.02)(0.55) + (0.03)(0.35) + (0.05)(0.1) = ....

    Therefore Pr(A | Error) = ......
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