Question

Eben rolls two standard number cubes 36 times. Predict how many times he will roll a sum of 4.

Answer 1

lets make a list
assuming they have 2 cubes with 1-6 on them
combos are
1,1
1,2
1,3
1,4
1,5
1,6
2,1
2,2
2,3
2,4
2,5
2,6
3,1
3,2
3,3
3,4
3,5
3,6
4,1
4,2
4,3
4,4
4,5
4,6
5,1
5,2
5,3
5,4
5,5
5,6
6,1
6,2
6,3
6,4
6,5
6,6


out of all 36 times, only 3 times did the sum equal 4
3 times he will roll a 4

Answer 2

The way to get a sum of 4 with two number cubes is getting:
1 and 3
2 and 2
So that is 1/6 for each number, that needs to be multiplied by itself, that is (1/6)(1/6) = 1/36, but two times because we do have two different combinations that can sum up to 4, so the total probability is:
2(1/36) = 2/36 = 1/18
So the probability is getting any of those combinations that sum 4 is one out of 18, if we double each quantity, the probability is equivalent to say 2 out of 36