Consider a firm that has two assembly lines, 1 and 2, both producing calculator. Assume that you hav

Discussion in 'Calculator Requests' started by math_celebrity, Jan 7, 2017.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    Consider a firm that has two assembly lines, 1 and 2, both producing calculator. Assume that you have purchased a calculator and it turns out to be defective. And the line 1 produces 60% of all calculators produced.

    L1: event that the calculator is produced on line 1
    L2: event that the calculator is produced on line 2

    Suppose that your are given the conditional information:
    10% of the calculator produced on line 1 is defective
    20% of the calculator produced on line 2 is defective

    Q: If we choose one defective, what is the probability that the defective calculator comes from Line 1 and Line2?

    L1 = event that the calculator is produced on line 1 = 0.6
    L2 = event that the calculator is produced on line 2 = 1 - 0.6 = 0.4
    D = Defective
    D|L1 Defective from Line 1 = 0.1
    D|L2 = Defective from Line 2 = 0.20

    Defective from Line 1
    P(L1|D) = P(L1)P(D/L1) / [ P(L1)P(D/L1) + P(L2)P(D/L2)]
    P(L1|D) = (.60)(.10) /[(.60)(.10)+ (.40)(.20)]
    P(L1|D) = 0.4286

    Defective from Line 2
    P(L2|D) = P(L2)P(D/L2) / [ P(L1)P(D/L1) + P(L2)P(D/L2)]
    P(L2|D) = (.40)(.20) /[(.60)(.10)+ (.40)(.20)]
    P(L2|D) = 0.5714

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