# binomial probability question

**URL:** <https://boards.straightdope.com/t/binomial-probability-question/151235>\
**Category:** Factual Questions\
**Created:** [January 27, 2003, 2:49pm UTC](https://boards.straightdope.com/t/binomial-probability-question/151235 "2003-01-27T14:49:00Z")\
**Posts on this page:** 2\
**Page:** 2

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**Author:** ![Pleonast](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pleonast/32/1183_2.png) [@Pleonast](https://boards.straightdope.com/u/Pleonast)\
**Post date:** [January 30, 2003, 1:52pm UTC](https://boards.straightdope.com/t/binomial-probability-question/151235/21 "2003-01-30T13:52:34Z")

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Referring to my Problem introduced above:_What if k = 0?_. If _N_\<=0, then _P_=0. Otherwise, _P_=1, since if we flip the coin, we’re guaranteed to have at least 0 tails. The boundary conditions should thus be

1. P(N,k) = 0 if N\<k or N\<=0.
2. P(N,k) = 1 if k\<=0.
3. P(k,k) = q^k if k\>0.

For the dice problem of **caffeine\_overdose** , a multinomial distribution is exactly what we’re looking for (as has been worked out above). If you’re going to deal with dice (or anything with more than a binary outcome) multinomials work great.

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**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\
**Post date:** [January 30, 2003, 3:51pm UTC](https://boards.straightdope.com/t/binomial-probability-question/151235/22 "2003-01-30T15:51:01Z")

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Actually, the simplest way to solve the die problem is to use a Markov chain. There are seven states, 0 through 6. When you’re in state n, you have a 5/6 probability of staying where you are, and a 1/6 chance of moving to state n + 1 (unless you’re in state 6–you always stay there). From there, it should be pretty simple to figure out how many rolls it should take you to get from state 0 to state 6.

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