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#1 2012-09-23 03:00:53

genericname
Member
Registered: 2012-05-16
Posts: 52

Statistic/Probability - Problems with ''at least'' in it

How do you go about solving problems like this? Is there a trick to it?

A class consists of 25 students, of whom 10 are women and the rest are men. We take a random sample of 5 students from this class. (Without replacement)
-What is the probability that the sample will include at least one woman?

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#2 2012-09-23 03:01:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,620

Re: Statistic/Probability - Problems with ''at least'' in it

Hi;

You use the hypergeometric distribution.

You will have to sum 5 different terms all involving the hypergeometric distribution. In summation notation it looks like this:


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2012-09-23 04:02:14

genericname
Member
Registered: 2012-05-16
Posts: 52

Re: Statistic/Probability - Problems with ''at least'' in it

Is it safe to assume that we use the formula only if it has "at least" in the question?

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#4 2012-09-23 04:07:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,620

Re: Statistic/Probability - Problems with ''at least'' in it

Hi;

Is it safe to assume that we use the formula only if it has "at least" in the question?

An "at least" in the problem implies a range of values in this case1 to 5. So, you will have to sum 5 hypergeometric terms that is why there is a sum there.

This is the formula:

You could us for say exactly 5 women by saying low = 5 and high = 5. Then you would be summing only one term.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#5 2012-09-23 10:02:25

genericname
Member
Registered: 2012-05-16
Posts: 52

Re: Statistic/Probability - Problems with ''at least'' in it

Thank you, Bobby.

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#6 2012-09-23 10:05:29

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,620

Re: Statistic/Probability - Problems with ''at least'' in it

Your welcome. May the computing be with you.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#7 2012-09-23 14:40:01

genericname
Member
Registered: 2012-05-16
Posts: 52

Re: Statistic/Probability - Problems with ''at least'' in it

Hi, another question:
An instructor gives an exam with 14 questions. Students are allowed to choose any 10 of them to answer. Suppose 6 questions require proof and 8 do not:
-How many groups of 10 questions contain at least one that require a proof?

I got 1736 as an answer. Is that correct?

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#8 2012-09-23 18:18:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,620

Re: Statistic/Probability - Problems with ''at least'' in it

Hi genericname;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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