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I have completely forgotten my statistics knowledge, and I have now found myself in dire need of this without having access to my books.

While I'm pursuing another context, I would like to ask my questions using marbles. Say I've got $100$ marbles of two colors: $6$ black marbles and $94$ white marbles. Then I pick $4$ marbles at random without putting them back. How do I then calculate the probability that $1$ marble is black, $2$ marbles are black, and $3, 4...$?

I feel there should exist some kind of a formula for calculating this probability. I want to be able to plot these probabilities via this formula.

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1 Answer 1

up vote 2 down vote accepted

Hints:

  • The number of ways of picking 4 marbles out of 100 (order unimportant) is ${100 \choose 4}$. This accounts for the "without replacement" specification since the $4$ marbles are distinct.

  • The number of ways of picking, for example, 2 white marbles and 2 black marbles out of the specified 100 marbles is ${6 \choose 2}{94 \choose 2}$.

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