How to calculate dice probability?

nossrannug · April 18th, 2011, 04:07 AM

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?

aswoods · April 18th, 2011, 06:21 AM

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 ${5\choose n}=\frac{5!}{n!(5-n)!}$ .

nossrannug · April 18th, 2011, 08:10 AM

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?

aswoods · April 18th, 2011, 08:27 AM

You just sum over the range. So to find the probability of at least 3, you sum the probabilities for 3, 4, and 5.

nossrannug · April 18th, 2011, 04:20 PM

Works like a charm

Again thank you so much for your help.

April 18th, 2011, 04:07 AM	#1
nossrannug 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?
$nossrannug is offline$

April 18th, 2011, 06:21 AM	#2
aswoods 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 ${5\choose n}=\frac{5!}{n!(5-n)!}$ .
$aswoods is offline$

April 18th, 2011, 08:27 AM	#4
aswoods 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.
$aswoods is offline$

April 18th, 2011, 04:20 PM	#5
nossrannug 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.
$nossrannug is offline$

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