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Math Help - Probability Problem... (check, please!)

  1. #1
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    Probability Problem... (check, please!)

    I just wanted to know if I'm in the right direction because, well, statistics class hates me!

    "The owner of a Auto-Parts Store has four employees (K, L, M, N) that make make mistakes in the preparation of a Sales Order in the following ratio: 1 to 20; 1 to 10; 1 to 10 and 1 to 20, respectively. Of all the orders prepared by K, L, M, N they are 20%; 60%; 15% and 5%, respectively. If an error occurs in an order, what are the probabilities that they were prepared by K, L, M, N?"

    For "K", there's a 1 out of 20 chance that he made the mistake. That's a 5%. Times that by the percent of all sales orders they do (20%) and you get there's a (1%) chance that he made the mistake................ right?

    Thank you!
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  2. #2
    Senior Member Sambit's Avatar
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    Do you know Bayes' Theorem?
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  3. #3
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    Hello, Tall Jessica!

    The owner of a Auto-Parts Store has four employees (K, L, M, N)
    that make make mistakes in sales orders in the following ratios:
    . . 1 to 20; 1 to 10; 1 to 10 and 1 to 20, respectively.

    K, L, M, N, prepare: 20%, 60%, 15%, and 5% or the orders, respectively.

    If an error occurs in an order, what are the probabilities
    . . that they were prepared by K, L, M, N?

    For K, there's a 1 out of 20 chance that he made the mistake; that's 5% . . .
    times the percent of all sales orders he does (20%) and you get:
    . . there's a 1% chance that he made the mistake, right?

    Right! . . . You got it!

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  4. #4
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    Probabilities are calculated from odds (or odds-rations) by taking the means of success/failure (1 in this case) and dividing by the total outcomes (1+20=21). So the probability K makes an error should be 1/21 or 0.0476.

    Now finding the total number of errors K makes is a matter of multiplying the total volume or orders she processes (represented as a proportion in this case), by the probability of her making an error; however that only gives you the probability she makes an order and its a faulty one. What they are asking you is, KNOWING that some error was made, what is the probability it was made by K. So you need to adjust your sample space - you are moving from ALL orders (bad and good), to simply the bad orders. As Sambit mentioned, you would need to apply Bayes Theorem here, with your new sample space consisting of bad orders, and finding out whats the probability of K having made such an order.

    The number should be larger than what you've got.
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