# More Probability !!

**URL:** <https://boards.straightdope.com/t/more-probability/39071>\
**Category:** Factual Questions\
**Created:** [October 31, 2000, 12:41pm UTC](https://boards.straightdope.com/t/more-probability/39071 "2000-10-31T12:41:39Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![MadHatter](https://avatars.discourse-cdn.com/v4/letter/m/f6c823/32.png) [@MadHatter](https://boards.straightdope.com/u/MadHatter)\
**Post date:** [October 31, 2000, 12:41pm UTC](https://boards.straightdope.com/t/more-probability/39071/1 "2000-10-31T12:41:39Z")

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Seeing as we have finally fought some ignorance in a different probabilty thread, I think it’s time for another one.

Assume someone takes a coin and tosses it in to the air 100 times. Also assume that the chances of a head or a tail coming up are exactly 50/50.

What are the odds that after 100 tosses of the coin, the result will be 50 heads and 50 tails?

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**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\
**Post date:** [October 31, 2000, 1:19pm UTC](https://boards.straightdope.com/t/more-probability/39071/2 "2000-10-31T13:19:30Z")

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The probability that the first fifty tosses are heads and the last fifty tosses are tails is pretty clearly (1/2)[sup]100[/sup].

Then there’s C(100,50) (binomial coefficient) different ways to pick which 50 of the 100 tosses are going to be heads, so the probability there’s exactly 50 heads is

C(100,50) \* (1/2)[sup]100[/sup], which is about 7.9589%.

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**Author:** ![MadHatter](https://avatars.discourse-cdn.com/v4/letter/m/f6c823/32.png) [@MadHatter](https://boards.straightdope.com/u/MadHatter)\
**Post date:** [October 31, 2000, 1:21pm UTC](https://boards.straightdope.com/t/more-probability/39071/3 "2000-10-31T13:21:40Z")

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> [@](#):
>
> \*Originally posted by Cabbage \*  
> \*\*The probability that the first fifty tosses are heads and the last fifty tosses are tails is pretty clearly (1/2)[sup]100[/sup].
> 
> Then there’s C(100,50) (binomial coefficient) different ways to pick which 50 of the 100 tosses are going to be heads, so the probability there’s exactly 50 heads is
> 
> C(100,50) \* (1/2)[sup]100[/sup], which is about 7.9589%. \*\*

**BZZZZZZZZZ!!!**

Wrong Answer !!!

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<div class="post-metadata">

**Author:** ![MadHatter](https://avatars.discourse-cdn.com/v4/letter/m/f6c823/32.png) [@MadHatter](https://boards.straightdope.com/u/MadHatter)\
**Post date:** [October 31, 2000, 1:45pm UTC](https://boards.straightdope.com/t/more-probability/39071/4 "2000-10-31T13:45:11Z")

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The answer I get is about 1 in 12.7

I misread your answer. I think 8% is about 1 in 12.7…