How to calculate odds in excel (for instance matching pairofdice)

[Diceroller]

How can one easily calculate the probability of several dice forming a pair
or two pair etc ?

For instance the chance of rolling a 10 on a 10-sided die is 1 in 10 (10%)
but it gets to complicated for me to calculate the chance of say two pair
(any) when rolling 10 dice.

Thanks in advance

 

[Arvi Laanemets]

Hi

The summary probability of two independet events equals with multiple of
probabilities for those events. I.e. for your example 0.1*0.1=0.01 = 1%

 

[aidan.heritage]

Not sure if it helps, but you MIGHT want to check out the COMBIN
function?

 

[Diceroller]

Thanks for the help but how would this work with larger equations ?
Ie having 10 dice and trying to calculate the odds of getting one pair,
which I think is somewhere around 99%)
However I don't know how to 'program' this into Excel.

 

[David Biddulph]

"Arvi Laanemets" wrote:

Thanks for the help but how would this work with larger equations ?
Ie having 10 dice and trying to calculate the odds of getting one pair,
which I think is somewhere around 99%)
However I don't know how to 'program' this into Excel.

The probability of not getting a pair when you roll the second die is 90%
[there are 9 numbers that don't match, and one that does.]
If you don't get a pair with the 2nd, then when you roll the 3rd die, the
further probability then is 80% [there are 8 numbers which don't match, and
2 that do match one or other of the numbers already thrown.]

If you follow this on, the probability of not throwing a pair with 10 dice
is =0.9*0.8*0.7*0.6*0.5*0.4*0.3*0.2*0.1, which is about 0.036%.
You thus have 99.964% probability of throwing at least one pair.

 

[Diceroller]

Thank you, this shortens the calculation, yet I can't seem to tweak this for
use with for instance a three of a kind roll ? OR how to chance increases for
a higher pair when you have more dice to throw.

"Arvi Laanemets" wrote:

Thanks for the help but how would this work with larger equations ?
Ie having 10 dice and trying to calculate the odds of getting one pair,
which I think is somewhere around 99%)
However I don't know how to 'program' this into Excel.

The probability of not getting a pair when you roll the second die is 90%
[there are 9 numbers that don't match, and one that does.]
If you don't get a pair with the 2nd, then when you roll the 3rd die, the
further probability then is 80% [there are 8 numbers which don't match, and
2 that do match one or other of the numbers already thrown.]

If you follow this on, the probability of not throwing a pair with 10 dice
is =0.9*0.8*0.7*0.6*0.5*0.4*0.3*0.2*0.1, which is about 0.036%.
You thus have 99.964% probability of throwing at least one pair.