Elizabeth has two identical number cubes both cubes have faces number one through six. If Elizabeth rolls each cube wants what is the probability that the sum of the two numbers on the top face will be 10
There are several ways to approach this problem, but one common method is to use a table to list all possible outcomes and count the ones that satisfy the given condition. Here is an example of such a table:
Cube 1 | Cube 2 | Sum
-------|--------|-----
1 | 1 | 2
1 | 2 | 3
1 | 3 | 4
1 | 4 | 5
1 | 5 | 6
1 | 6 | 7
2 | 1 | 3
2 | 2 | 4
2 | 3 | 5
2 | 4 | 6
2 | 5 | 7
2 | 6 | 8
3 | 1 | 4
3 | 2 | 5
3 | 3 | 6
3 | 4 | 7
3 | 5 | 8
3 | 6 | 9
4 | 1 | 5
4 | 2 | 6
4 | 3 | 7
4 | 4 | 8
4 | 5 | 9
4 | 6 | 10
5 | 1 | 6
5 | 2 | 7
5 | 3 | 8
5 | 4 | 9
5 | 5 | 10
5 | 6 | 11
6 | 1 | 7
6 | 2 | 8
6 | 3 | 9
6 | 4 | 10
6 | 5 | 11
6 | 6 | 12
In this table, each row represents a possible outcome of rolling the two cubes, showing the number on the top face of Cube 1, the number on the top face of Cube 2, and their sum. There are 6 × 6 = 36 possible outcomes in total, as each cube can land on any of its six faces independently of the other. To find the probability of getting a sum of 10, we need to count the number of outcomes where the sum is 10, and divide by the total number of outcomes:
Number of outcomes with sum 10: 3 (from the row highlighted in bold)
P(sum = 10) = 3/36 = 1/12
Therefore, the probability that Elizabeth rolls each cube and the sum of the two numbers on the top face will be 10 is 1/12.