Question

in a certain dice game, three fair dice are rolled and the total on all three dice are counted. Let the random variable x be the total count on all three dice. construct the probability distribution for x.

Answer 1

The total count is the sum of all three dice, right?

Answer 2

theres a nice formula to generate the sum of n dice

Answer 3

the sample space here has 216 points. let me give you some of the space

space = { (1,1,1) (1,1,2) (1,1,3) (1,1,4) ... }
now if you add these number 1 + 1 + 1 , 1 + 1 + 2 ,
sum space ={ 3,4,5,6,7,8,9,10

Answer 4

the sample space here has 216 points.
let me write out some of the space for (die1, die2, die3)
space = { (1,1,1) (1,1,2) (1,1,3) (1,1,4) ... (6,6,5) (6,6,6)}

now if you add these numbers in the space 1+1+1 , 1+1+2 , etc, we get
sum space ={ 3,4,5,6,7,8,9,10, ... 18}