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.

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.

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?

Quote:

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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?

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Yes it dose. You made it seem so much clearer. Thank You, now I'll still have some hair left:)

Quote:

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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.

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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:)

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,