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Statistics Anyone?

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Last Modified: 2012-05-06
Folks,

Let's say I have two dice and I say to everyone around me, "If I roll a five, I'll do thus and such".  I roll the first time and get a three and a two.  Attributing it t coincidence, I roll again and get a five and a one.  Perturbed, I roll just one die and get a five.

What are the odds of this?
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Commented:
assuming a set of standard 6-sided dice with equal probability of any faces coming up...

odds of a 3 and a 2 are 1/6 x 1/6 or 1/36
odds of a 5 and a 1 are 1/6 x 1/6 or 1/36 for a combined probability of 3,2,5,1: 1/36 x 1/36= 1/1296
odds of a 5 with just one die are 1/6  for combined probabilility of 3,2,5,1,5:  1/1296 x 1/6 = 1/ 7776 or approximately 1 hundredth of 1 percent chance

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Sean StuberDatabase Developer & Administrator
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Commented:
the above does assume each die is distinct though.

if they are not distinct  (that is a 3 on one die and 2 on the other is the same as a 2 on the first and a 3 on the second) then...

3,2 :   2/6 x 1/6 = 1/18
5,1 :   2/6 x 1/6 = 1/18
5    :   1/6

multiplying the all together and you get:  1/1944 or approximatlye 1 twentieth of 1 percent chance
ozo
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Commented:
define "this"
was there any chance that you might have said "If I roll a four, I'll do such and thus". ?
would that count as part of "this"
if the only thing that counts as "this" is getting exactly a
three and a two.
then a
five and a one
then a five
then the odds would be
1/1944
Commented:
(2/36) X (2/36) X (1/6)  = 4/7776 = 1/1944

about 1 in 2000

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Commented:
Thanks.  I guess my marriage is built on a solid foundation then.
Sean StuberDatabase Developer & Administrator
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Commented:
dqmq,  can you explain your numbers?
ozo
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Commented:
If "this" means two rolls of a pair of dice, and one roll of a single die, each of which either contains a 5 or has a total of 5, then the odd are
25/864
Sean StuberDatabase Developer & Administrator
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Commented:
ozo, how did you get that?

If I counted correctly, I get...

16/36 * 16/36 * 1/6 = 256/7776
Sean StuberDatabase Developer & Administrator
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Commented:
where 36 = number of possibilities with 2 dice
16 = 12 (number of possible ways to get a "5" with 2 dice) + 4 (number of possible ways to get a sum of 5 with 2 dice)

squared because you do it twice and 1/6 for the odds of getting a 5 with one die

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Commented:
These are standard, identical 6-sided dice.  
ozo
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Commented:
15 = 11 (number of possible ways to get a "5" with 2 dice) + 4 (number of possible ways to get a sum of 5 with 2 dice)
Sean StuberDatabase Developer & Administrator
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Commented:
ah,  I counted 5,5 twice.

thanks!

Commented:
With two dice, there are 36 possible combinations, 4 of these will give the result of  "5".
1 and 4, 2 and 3, 3 and 2, 4 and 1. So odds of rolling a total of five with 2 dice is 4/36 = 1/9.
With one die, there are six possible combinations, and only one that results in a "5" so odds are 1/6
So odds of rolling a five twice with 2 dice, then once with a single die are 1/9 x 1/9 x 1/6 = 1/486. around 0.2%

If you include as well the possibility of one die turning up a five when rolling two dice, as well as a total result of five, there are 15 possible "5" combinations
1 and 4, 2 and 3, 3 and 2, 4 and 1, 1 and 5, 2 and 5, 3 and 5, 4 and 5, 5 and 5, 6 and 5, 5 and 6, 5 and 4, 5 and 3, 5 and 2, 5 and 1, so odds are only 15/36 =  5/12. so odds of rolling a "5" twice with two dice, and once with one die is 5/12 x 5/12 x 1/6 = 25/864 about 1/34.56, around 3%

Two get exactly the results you quoted, i.e 3 and 2, followed by 1 and 5, followed by a single die 5, odds are 2/36 (for a 2 and 3) x 2/36 (for a 1 and 5) x 1/6 for a single 5 = 1/18 x 1/18 x 1/6 = 1/1944,
around 0.05%
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