Two number cubes labeled 1-6 are rolled.Which set represents the sample space for all the possible outcomes of the sum shown on both number cubes?

Question

A) (1,2,3,4,5,6) ,(B) (1,2,3,4,5,6,7,8,9,10,11,12),(C) (2,3,4,5,6,7,8,9,10,11,12) ,(D) (2,3,4,5,6,7,8,9,10,11)

Answer 1

Hello Victor,

First, here's the sample space for cube 1: {1,2,3,4,5,6}

It's the same sample space for cube 2: {1,2,3,4,5,6}

For the sample space showing all possible outcomes for the sum of both cubes:

1. It can be as low as the sum of the lowest numbers for each cubes: 1+1 = 2 is the where the sample space would begin.
2. The sum can also go as high as the sum of the highest numbers for both cubes: 6+6 = 12 is where the sample space would end.
3. It will also include all numbers in-between, that means: 3,4,5,6,7,8,9,10,11

Put all that together, and the sample space for the sum of both cubes is: {2,3,4,5,6,7,8,9,10,11,12} which is answer choice (C).

Cheers.