# Die With Multiple Same Sides

#### ElizaSells

##### New Member
Hi everyone - see my problem below. With a regular die I know my denominator is 36 for each probability. What I'm wondering here is if that changes since multiple sides of the die have the same number... Right now I have the probability of a sum of 2 is 1/36, a sum of 3 as 2/36, sum of 4 as 3/36, etc. Do you think that I need to adjust my denominator to take into account the repetitive sides? All opinions are very much appreciated.

#### Dason

##### Ambassador to the humans
When rolling two 'regular' die... why is the denominator for the probabilities 36? Can you explain why?

#### ElizaSells

##### New Member
There are 36 possible combinations of rolls when rolling two regular die. 6^2. I’m not sure if I’m this case I should do 6^2 or something else, since Dice a and b are different

#### ElizaSells

##### New Member
Is it just 4x 6 instead of 6x6 you think?

#### Buckeye

##### Member
First, I would define the random variable of interest. Then find all of the possible value that the random variable can take (and how these values come about). The part in parenthesis might help you think about the probabilities. Then use the definition of expectation and variance.

#### ElizaSells

##### New Member
Ah yes, I know the random variable is the sum, I’ve mapped out all the ways we can get each sum. I’m just not sure (for example) if the first 2 on dice A paired with any of the numbers on dice b is different from the second 2 on dice a paired with any number on dice b. I understand the problem and what it’s asking and what expectation and variance is just not sure about this small piece that’s essential to finding those things!

#### Buckeye

##### Member
So, to get a sum of 3 you would need a 2 from die A and a 1 from die B. That probability is (2/6)*(1/6). Because of independence of the dice.