# Simple math question

**URL:** <https://boards.straightdope.com/t/simple-math-question/352579>\
**Category:** Factual Questions\
**Created:** [April 13, 2006, 9:18pm UTC](https://boards.straightdope.com/t/simple-math-question/352579 "2006-04-13T21:18:47Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![VarlosZ](https://avatars.discourse-cdn.com/v4/letter/v/d78d45/32.png) [@VarlosZ](https://boards.straightdope.com/u/VarlosZ)\
**Post date:** [April 13, 2006, 9:18pm UTC](https://boards.straightdope.com/t/simple-math-question/352579/1 "2006-04-13T21:18:47Z")

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Say I had a bet whereby I had to win at least 5 out of 6 coin flips. Short of manually adding up every possible outcome of the series of flips, how would I go about figuring my odds of winning? Thanks.

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**Author:** ![bup](https://avatars.discourse-cdn.com/v4/letter/b/6bbea6/32.png) [@bup](https://boards.straightdope.com/u/bup)\
**Post date:** [April 13, 2006, 9:24pm UTC](https://boards.straightdope.com/t/simple-math-question/352579/2 "2006-04-13T21:24:15Z")

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There are 7 ways you can win:

WWWWWL  
WWWWLW  
WWWLWW  
WWLWWW  
WLWWWW  
LWWWWW  
WWWWWW

There are 2[sup]6[/sup] total sequences of a coin flipped 6 times.

7/64

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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:** [April 13, 2006, 9:36pm UTC](https://boards.straightdope.com/t/simple-math-question/352579/3 "2006-04-13T21:36:47Z")

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The solution is given by the binomial distribution with n = 6, p = .5. So P(X\>=5) = 1- P(X\<=4) = 1 - .8906 = .1094, about 11%.