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    pepperjay's Avatar
    pepperjay Posts: 3, Reputation: 1
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    #1

    Mar 25, 2008, 08:09 PM
    Hiring Probability
    Question:
    Of 64 qualified applicants for job classification B, 16 have long hair. In the past the agency hired 8 positions. If the agency hired without regard to hair length, what is the probability of hiring 7 people with long hair out of the eight new hires? Would you say that the agency discriminated?

    In order to solve the problem, I need n ( the number of trials), r ( the number of successes) p ( the probability that the event will be a success and q( 1-p).

    Here is my problem. I think that r = 7, because the problem states that we want to know about hiring 7 long hairs out of 8 openings. Is this correct?

    I think that n = 16 because even though there are 64 qualified applicants, only 16 of them have long hair. Is this correct?

    I am so unsure of p. I'm not sure if it is 7/64, because we want 7 out of the 64 to get hired, or if it is 7 out of 8, because we want 7 of the 8 new hires to have long hire.

    Please help, I am pulling my hair out over this one.
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #2

    Mar 26, 2008, 05:03 AM
    This appears to be a hypergeometric distribution.

    Given a population of N items with k successes and N-k failures, the probability of selecting a sample of size n that has x successes and n-x failures is given by



    N=64, k=16, n=8, x=7.

    Can you put it together using the formula? Intuitively, one would think the probability is rather low. Much less than 7/64.
    rodandy12's Avatar
    rodandy12 Posts: 227, Reputation: 24
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    #3

    Mar 26, 2008, 05:25 AM
    Frequently the issue with problems like this is getting through the mumbo jumbo. I bet you have had some problems where you had black and white beads in a jar that you couldn't see through. This problem is like that.

    We know the ratio of black beads (long hair) to white beads (others) in the jar... 1:4 (16:64). Now you are drawing at random eight beads. You are being asked what the probability is that seven of them are black beads.

    Does this help?
    pepperjay's Avatar
    pepperjay Posts: 3, Reputation: 1
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    #4

    Mar 26, 2008, 09:36 AM
    Quote Originally Posted by rodandy12
    Frequently the issue with problems like this is getting through the mumbo jumbo. I bet you have had some problems where you had black and white beads in a jar that you couldn't see through. This problem is like that.

    We know the ratio of black beads (long hair) to white beads (others) in the jar...1:4 (16:64). Now you are drawing at random eight beads. You are being asked what the probability is that seven of them are black beads.

    Does this help?
    Yes it dose. You made it seem so much clearer. Thank You, now I'll still have some hair left:)
    pepperjay's Avatar
    pepperjay Posts: 3, Reputation: 1
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    #5

    Mar 26, 2008, 09:42 AM
    Quote Originally Posted by galactus
    This appears to be a hypergeometric distribution.

    Given a population of N items with k successes and N-k failures, the probability of selecting a sample of size n that has x successes and n-x failures is given by



    N=64, k=16, n=8, x=7.

    Can you put it together using the formula?. Intuitively, one would think the probability is rather low. Much less than 7/64.

    The formula was different from mine, but it is still kind of the same. I think it's more advanced, but it helped me break the stuff down by reading the breakdown you gave. Thanks much:)
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #6

    Mar 26, 2008, 12:50 PM
    If you think about it a little, you really don't need the fancy-schmancy formula.

    There are 64 people in all from which we are choosing 8. 48 with short hair and 16 with long hair.

    We are choosing 7 of the 16 long hairs and 1 of the 48 short hairs.

    Therefore,
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