Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
up vote 2 down vote accepted


  • 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 ${6 \choose 2}{94 \choose 2}$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.