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April 18th, 2011, 03:07 AM   #1
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How to calculate dice probability?

Hello all,
I've got a problem with calculating dice probability.
Lets say I have 5d20 (5 dice and each dice has 20 sides). Now I need to calculate the probability that 1, 2, 3, 4, 5 of the dice are x or higher.
If we make x = 14. Then I know that the chances that none of the dice are >= 14 is: (13/20)^5 = 11.6%.
So the chances that at least one if them is >= 14 is: 1 - 0.116 = 88.4%.
And I know that the chance of getting all of the dice >= 14 is: (7/20)^5 = 0.5%.

If I want to calculate what the chances are that 2 dice are >= 14 how would I do that? what about 3 dice? Does anyone know of a formula that I can just put my numbers into and get the result?
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April 18th, 2011, 05:21 AM   #2
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Re: How to calculate dice probability?

If you roll 5d20, the chance that exactly n dice are x or higher is
where .
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April 18th, 2011, 07:10 AM   #3
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Re: How to calculate dice probability?

Quote:
Originally Posted by aswoods
If you roll 5d20, the chance that exactly n dice are x or higher is
where .
Thank you so much. i knew I was suppose to use a ! somewhere :P
Another question. Is there a formula that calculates at least instead of exactly?
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April 18th, 2011, 07:27 AM   #4
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Re: How to calculate dice probability?

You just sum over the range. So to find the probability of at least 3, you sum the probabilities for 3, 4, and 5.
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April 18th, 2011, 03:20 PM   #5
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Re: How to calculate dice probability?

Works like a charm
Again thank you so much for your help.
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