Formula to calculate the probability of rolling an N-sided die M times and getting X or more of any single number?

Asked Dec 07 '21 at 08:46

Active Dec 08 '21 at 16:52

Viewed 62 times

Let's say I have a fair 12-sided die. If I roll it 8 times, you can calculate the odds of rolling any single number, say, 4 or more times.

Running a simulation, I get that it's about p≈0.031

What, then, is the formula to calculate the probability of rolling a fair N-sided die M times and getting any single number X or more times?

This isn't a homework question. The specific example came up in a project I was working on, and I would like to have a formula for the general case instead of having to run simulations.

edited Dec 08 '21 at 16:52

asked Dec 07 '21 at 08:46

Brad Spendlove

1

Hint: the binomial distribution. – user2974951 Dec 07 '21 at 08:51
1

Please add the [tag:self-study] tag & read its wiki. Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. Please make these changes as just posting your homework & hoping someone will do it for you is grounds for closing. – kjetil b halvorsen Dec 07 '21 at 19:40
Does this answer your question? Probability of throwing n different numbers in m throws of a dice – Carl Dec 09 '21 at 19:49

Formula to calculate the probability of rolling an N-sided die M times and getting X or more of any single number?

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