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If you have a group of 5 boys and 5 girls and you take a random sample of 5 what is the distribution of results of number of boys 0,1,2,3,4,5?

If you had a very large equal number of boys and girls it would be the binomial distribution. How would it differ and how to calculate probabilities of each number of boys using this small total number?

Parcly Taxel
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RMR
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    I think you have it the wrong way around: The binomial distribution is the exact distribution here, and it becomes a normal distribution in the limit. – Bobson Dugnutt May 13 '17 at 01:06

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This can be rephrased in one of the classic wordings. There are 5 good items and 5 bad items in a box. I think it's implied that you are draw without replacement. Let $X$ count the number of good items that you draw. Does this sound familiar?

This follows the

Hypergeometric distribution with $P(X = k) = \frac{\binom{5}{k}\binom{5}{5-k}}{\binom{10}{5}}.$

Em.
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