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 April 18th, 2011, 04:07 AM #1 Newbie   Joined: Apr 2011 Posts: 3 Thanks: 0 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?
 April 18th, 2011, 06:21 AM #2 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: How to calculate dice probability? If you roll 5d20, the chance that exactly n dice are x or higher is $\frac{{5\choose n}(21-x)^n(x-1)^{5-n}}{20^5}$ where ${5\choose n}=\frac{5!}{n!(5-n)!}$.
April 18th, 2011, 08:10 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 $\frac{{5\choose n}(21-x)^n(x-1)^{5-n}}{20^5}$ where ${5\choose n}=\frac{5!}{n!(5-n)!}$.
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?

 April 18th, 2011, 08:27 AM #4 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 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.
 April 18th, 2011, 04:20 PM #5 Newbie   Joined: Apr 2011 Posts: 3 Thanks: 0 Re: How to calculate dice probability? Works like a charm Again thank you so much for your help.

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