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Suppose that I roll a six sided die $x$ times, say 10, what is the probability that I will get a particular side/number, say 6, a specific number of times? Is there a general formula to compute this?

For example, what is the probability that I will:

  • Get exactly 1 time six
  • Get exactly 2 times six
  • Get exactly 3 times six
  • $\dots$
  • Get exactly 10 times six
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It's a binary outcome for each, correct? Either you have a success (ie. roll a six), or you have a failure (ie. roll a 'not six'). Your probability of success is $\frac{1}{6}$, and you can decide your number of trials $n$, and number of successes, $k$ for which you want to calculate an answer. Here's the wikipedia description of a binomial distribution. That should get you where you're going.

http://en.wikipedia.org/wiki/Binomial_distribution

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