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Math Help - Random selection without replacement.

  1. #1
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    Random selection without replacement.

    In a certain factory, machines I, II, III are all producing springs of the same length. Machines I, II, and III produce 1%, 4% and 2% defective springs, respectively. Of the total production of springs in the factory, Machine I produces 30%, Machine II products 25%, and Machine III produces 45%. If one spring is selected at random from the total springs produced in a given day, determine the probability that it is defective.

    I know that this must involve the intersection of the percentages of defective springs given those produced by the machines, but I can't put it together. Will someone please help me get started? Thanks.
    Last edited by mr fantastic; September 3rd 2011 at 01:33 AM. Reason: Re-titled.
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  2. #2
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    Re: Probability Question

    I think I might just produce 1000 springs and see how it goes.

    I: 1000 * 0.30 = 300, then 300 * 0.01 = 3
    II: 1000 * 0.25 = 250, then 250 * 0.04 = 10
    III: 1000 * 0.45 = 450, then 450 * 0.02 = 9

    In 1000 springs, we have 22 defectives. No what?
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  3. #3
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    Re: Probability Question

    Aha! Thank you; the number of springs produced does seem to be the magic number I was missing. I'll try that and see what I can do. Thank you, again, for your help.
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