Die With Multiple Same Sides

#1
Hi everyone - see my problem below.
Capture.JPG

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
#2
When rolling two 'regular' die... why is the denominator for the probabilities 36? Can you explain why?
 
#3
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
 
#5
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.
 
#6
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!
 
#7
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.