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marc.t.davies@gmail.com science forum addict
Joined: 31 May 2006
Posts: 52

Posted: Thu Jul 20, 2006 2:18 pm Post subject:
Re: Probability of attaining a minimum value when rolling dice



Arthur Dent wrote:
Quote:  MTD wrote:
You could try approximating with a normal distrubtion. Calculating the
mean and the variance shouldn't be too hard...
Sounds like a good wheeze, but wouldn't you need to know the probabilty
of getting rolling exactly n?

I'm not sure what you mean. Rolling a total of N on N dice is (1/6)^N,
that's trivial. 

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marc.t.davies@gmail.com science forum addict
Joined: 31 May 2006
Posts: 52

Posted: Thu Jul 20, 2006 2:14 pm Post subject:
Re: Probability of attaining a minimum value when rolling dice



Quote:  The subject poses the question I was answering, the probability of
attaining a minimum value when rolling dice.

No, you answer how to calculate the probability of getting THE minimum
value for the total.
He asks for the probability of getting a total of _at least X _,
presumably with the condition n <= X < 6n 

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Virgil science forum Guru
Joined: 24 Mar 2005
Posts: 5536

Posted: Thu Jul 20, 2006 7:06 am Post subject:
Re: Probability of attaining a minimum value when rolling dice



In article <1153378650.631766.155800@75g2000cwc.googlegroups.com>,
"Proginoskes" <CCHeckman@gmail.com> wrote:
Quote:  Virgil wrote:
In article <1153234669.122030.181660@75g2000cwc.googlegroups.com>,
nick@blackmarble.co.uk wrote:
Hi All
If I roll N 6sided dice, whats the probability of scoring a total of
at least X?
Sorry if this is really simple, but my maths sucks :)
Nick
If each die has a single face with its smallest value on it and the dice
are "honest", then the probability of getting the lowest total on one
roll of n dice (or n rolls of one die) is (1/6)^n = 1/(6^n).
Evidently you need to read the post before you answer.
 Christopher Heckman

The subject poses the question I was answering, the probability of
attaining a minimum value when rolling dice. 

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Proginoskes science forum Guru
Joined: 29 Apr 2005
Posts: 2593

Posted: Thu Jul 20, 2006 6:57 am Post subject:
Re: Probability of attaining a minimum value when rolling dice



Virgil wrote:
Quote:  In article <1153234669.122030.181660@75g2000cwc.googlegroups.com>,
nick@blackmarble.co.uk wrote:
Hi All
If I roll N 6sided dice, whats the probability of scoring a total of
at least X?
Sorry if this is really simple, but my maths sucks :)
Nick
If each die has a single face with its smallest value on it and the dice
are "honest", then the probability of getting the lowest total on one
roll of n dice (or n rolls of one die) is (1/6)^n = 1/(6^n).

Evidently you need to read the post before you answer.
 Christopher Heckman 

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Proginoskes science forum Guru
Joined: 29 Apr 2005
Posts: 2593

Posted: Thu Jul 20, 2006 6:56 am Post subject:
Re: Probability of attaining a minimum value when rolling dice



Keith A. Lewis wrote:
Quote:  "Arthur Dent" <fd4scy@yahoo.co.uk> writes in article <1153239107.272078.318890@p79g2000cwp.googlegroups.com> dated 18 Jul 2006 09:11:47 0700:
MTD wrote:
You could try approximating with a normal distrubtion. Calculating the
mean and the variance shouldn't be too hard...
I don't think a normal distribution is a good approximation.
Sounds like a good wheeze, but wouldn't you need to know the probabilty
of getting rolling exactly n?
That's easy.
p(=n) = (6  n7) / 36 for 1<n<13
p(>=n) = 1  (n1)(n2)/72 for 1<n<=7
= (14n)(13n)/72 for 7<n<=13

That's with 2 dice; the OP asked the question for a general number of
dice.
 Christopher Heckman 

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marc.t.davies@gmail.com science forum addict
Joined: 31 May 2006
Posts: 52

Posted: Wed Jul 19, 2006 3:54 pm Post subject:
Re: Probability of attaining a minimum value when rolling dice



Quote:  Really? I think a normal distribution with mean 7*N/2 and variance
35*N/12 ought to be pretty reasonable for N greater than maybe about 5
or 6, and not ridiculously wrong even for N = 3 or 4. For larger N I
would expect it to get more and more accurate...

That's what I figured.
Hmm. If I have the time I will try to calculate the error factor. 

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bill11 science forum Guru
Joined: 07 Sep 2005
Posts: 311

Posted: Wed Jul 19, 2006 12:51 am Post subject:
Re: Probability of attaining a minimum value when rolling dice



nick@blackmarble.co.uk wrote:
Quote:  Hi All
If I roll N 6sided dice, whats the probability of scoring a total of
at least X?
Sorry if this is really simple, but my maths sucks :)
Nick

It is really simple, but very labor intensive.
Suppose that N = 10 and X =35. You would to list every combination of
10 dice that added up to 35. This you would hve to do manualy Then you
would have to permutate every combination to get the total number of
ways
of getting 35 with 10 dice.
Divide this total by the total number of ways of throwing 10 dice;
6^10 to get the probability of a sum of 35.
regards
Bill J
..
\ 

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matt271829news@yahoo.co. science forum Guru
Joined: 11 Sep 2005
Posts: 846

Posted: Wed Jul 19, 2006 12:34 am Post subject:
Re: Probability of attaining a minimum value when rolling dice



Keith A. Lewis wrote:
Quote:  "Arthur Dent" <fd4scy@yahoo.co.uk> writes in article <1153239107.272078.318890@p79g2000cwp.googlegroups.com> dated 18 Jul 2006 09:11:47 0700:
MTD wrote:
You could try approximating with a normal distrubtion. Calculating the
mean and the variance shouldn't be too hard...
I don't think a normal distribution is a good approximation.

Really? I think a normal distribution with mean 7*N/2 and variance
35*N/12 ought to be pretty reasonable for N greater than maybe about 5
or 6, and not ridiculously wrong even for N = 3 or 4. For larger N I
would expect it to get more and more accurate... 

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Virgil science forum Guru
Joined: 24 Mar 2005
Posts: 5536

Posted: Tue Jul 18, 2006 7:54 pm Post subject:
Re: Probability of attaining a minimum value when rolling dice



In article <1153234669.122030.181660@75g2000cwc.googlegroups.com>,
nick@blackmarble.co.uk wrote:
Quote:  Hi All
If I roll N 6sided dice, whats the probability of scoring a total of
at least X?
Sorry if this is really simple, but my maths sucks :)
Nick

If each die has a single face with its smallest value on it and the dice
are "honest", then the probability of getting the lowest total on one
roll of n dice (or n rolls of one die) is (1/6)^n = 1/(6^n). 

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Keith A. Lewis science forum Guru
Joined: 24 Mar 2005
Posts: 478

Posted: Tue Jul 18, 2006 6:55 pm Post subject:
Re: Probability of attaining a minimum value when rolling dice



"Arthur Dent" <fd4scy@yahoo.co.uk> writes in article <1153239107.272078.318890@p79g2000cwp.googlegroups.com> dated 18 Jul 2006 09:11:47 0700:
Quote: 
MTD wrote:
You could try approximating with a normal distrubtion. Calculating the
mean and the variance shouldn't be too hard...

I don't think a normal distribution is a good approximation.
Quote:  Sounds like a good wheeze, but wouldn't you need to know the probabilty
of getting rolling exactly n?

That's easy.
p(=n) = (6  n7) / 36 for 1<n<13
p(>=n) = 1  (n1)(n2)/72 for 1<n<=7
= (14n)(13n)/72 for 7<n<=13
Keith Lewis klewis {at} mitre.org
The above may not (yet) represent the opinions of my employer. 

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F_L_Palmer@yahoo.com science forum beginner
Joined: 12 Dec 2005
Posts: 4

Posted: Tue Jul 18, 2006 4:41 pm Post subject:
Re: Probability of attaining a minimum value when rolling dice



nick@blackmarble.co.uk wrote:
Quote:  Hi All
If I roll N 6sided dice, whats the probability of scoring a total of
at least X?
Sorry if this is really simple, but my maths sucks :)
Nick

Take the expansion of (A + B)^n [= A^n + B*A^(n1) + ... ]
A= 1/6 B=5/6
The first term is the probability of getting 6, the second term is the
probability of gettng 5. The sum of those terms is the probability of
getting at least five.
Keep going until you reach X.
This is much easier to write when you can use sigmas. 

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Arthur Dent science forum Guru Wannabe
Joined: 19 May 2005
Posts: 203

Posted: Tue Jul 18, 2006 4:12 pm Post subject:
Re: Probability of attaining a minimum value when rolling dice



MTD wrote:
Quote:  You could try approximating with a normal distrubtion. Calculating the
mean and the variance shouldn't be too hard...

Sounds like a good wheeze, but wouldn't you need to know the probabilty
of getting rolling exactly n? 

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Arthur Dent science forum Guru Wannabe
Joined: 19 May 2005
Posts: 203

Posted: Tue Jul 18, 2006 4:11 pm Post subject:
Re: Probability of attaining a minimum value when rolling dice



MTD wrote:
Quote:  You could try approximating with a normal distrubtion. Calculating the
mean and the variance shouldn't be too hard...

Sounds like a good wheeze, but wouldn't you need to know the probabilty
of getting rolling exactly n? 

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marc.t.davies@gmail.com science forum addict
Joined: 31 May 2006
Posts: 52

Posted: Tue Jul 18, 2006 3:52 pm Post subject:
Re: Probability of attaining a minimum value when rolling dice



You could try approximating with a normal distrubtion. Calculating the
mean and the variance shouldn't be too hard... 

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Patrick Coilland science forum Guru Wannabe
Joined: 29 Jan 2006
Posts: 197

Posted: Tue Jul 18, 2006 3:38 pm Post subject:
Re: Probability of attaining a minimum value when rolling dice



nick@blackmarble.co.uk nous a récemment amicalement signifié :
Quote:  Hi All
If I roll N 6sided dice, whats the probability of scoring a total of
at least X?
Sorry if this is really simple, but my maths sucks :)
Hello, 
I don't think there is a simple expression for the solution.
Il you call p(x,n) the number you are looking for, this number may be
computed in that way :
p(x,n) =
(p(x6,n1)+q(x5,n1)+q(x4,n1)+q(x3,n1)+q(x2,n1)+q(x1,n1))/6
with initialization : p(x,0) = 1 for x <= 0
p(x,0) = 0 for x > 0

Patrick 

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