# Probability of Dice

**URL:** <https://boards.straightdope.com/t/probability-of-dice/497508>\
**Category:** Factual Questions\
**Created:** [May 24, 2009, 11:51pm UTC](https://boards.straightdope.com/t/probability-of-dice/497508 "2009-05-24T23:51:21Z")\
**Posts on this page:** 7\
**Page:** 1

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**Author:** ![thwartme](https://avatars.discourse-cdn.com/v4/letter/t/ecc23a/32.png) [@thwartme](https://boards.straightdope.com/u/thwartme)\
**Post date:** [May 24, 2009, 11:51pm UTC](https://boards.straightdope.com/t/probability-of-dice/497508/1 "2009-05-24T23:51:21Z")

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Hey,

I suck at math, and would appreciate any help.

I know that if I’m rolling two dice (six-sided dice), the probability of getting a result of 7 is 1 in 6.

If I roll the pair four times, what is the probabilty of one of those results being a 7?

In other words how do I calculate the odds that a one-in-six chance will occur, given only four chances?

Thanks,  
thwartme

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**Author:** ![nivlac](https://avatars.discourse-cdn.com/v4/letter/n/3bc359/32.png) [@nivlac](https://boards.straightdope.com/u/nivlac)\
**Post date:** [May 25, 2009, 12:00am UTC](https://boards.straightdope.com/t/probability-of-dice/497508/2 "2009-05-25T00:00:28Z")

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This is a simple binomial problem with n=4, p=1/6. For exactly one instance that the dice will be a 7 the probability is .3858. For 1 or more instances, it’s .4823.

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**Author:** ![nivlac](https://avatars.discourse-cdn.com/v4/letter/n/3bc359/32.png) [@nivlac](https://boards.straightdope.com/u/nivlac)\
**Post date:** [May 25, 2009, 12:01am UTC](https://boards.straightdope.com/t/probability-of-dice/497508/3 "2009-05-25T00:01:56Z")

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Make that second probability .5178.

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**Author:** ![thwartme](https://avatars.discourse-cdn.com/v4/letter/t/ecc23a/32.png) [@thwartme](https://boards.straightdope.com/u/thwartme)\
**Post date:** [May 25, 2009, 12:05am UTC](https://boards.straightdope.com/t/probability-of-dice/497508/4 "2009-05-25T00:05:19Z")

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Thanks very much for your help.

Did I mention I suck at math? I just want to make sure I understand your answer…

If the “probability is .3858”, that means that 38.58 times out of a hundred, I can expect the result in question?

Or in other words, in four roles I’m likely to see one and only one 7 a little more than a third of the time, and two or more sevens almost half the time?

thanks,  
thwartme

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**Author:** ![Askance](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/askance/32/8281_2.png) [@Askance](https://boards.straightdope.com/u/Askance)\
**Post date:** [May 25, 2009, 1:38am UTC](https://boards.straightdope.com/t/probability-of-dice/497508/5 "2009-05-25T01:38:44Z")

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Yes and Yes.

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**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\
**Post date:** [May 25, 2009, 2:35am UTC](https://boards.straightdope.com/t/probability-of-dice/497508/6 "2009-05-25T02:35:56Z")

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The probabllity that you WON’T get a 7 in one roll is 5/6. The probability that it won’t happen four times in a row is (5/6)^4 which is 625/1296 or about 48.2% and the probability you will is 51.8%.

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**Author:** ![thwartme](https://avatars.discourse-cdn.com/v4/letter/t/ecc23a/32.png) [@thwartme](https://boards.straightdope.com/u/thwartme)\
**Post date:** [May 25, 2009, 3:27am UTC](https://boards.straightdope.com/t/probability-of-dice/497508/7 "2009-05-25T03:27:00Z")

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Awesome. Thanks very much.