Question

you are playing a game that involves 2 number cubes. What is the probability that the sum of the 2 cubes equals 8? write your answer as a simplified fraction

Answer 1

To find the probability that the sum of two number cubes (dice) equals 8, we need to first determine all the possible outcomes when rolling two dice and then determine how many of those outcomes result in a sum of 8.

1. **Total outcomes**: Each die has 6 faces, so the total number of outcomes when rolling two dice is:
\[
6 \times 6 = 36
\]

2. **Favorable outcomes for the sum of 8**: We can list the pairs of numbers on the dice that add up to 8:
- (2, 6)
- (3, 5)
- (4, 4)
- (5, 3)
- (6, 2)

Thus, we have the following combinations that give a sum of 8:
- (2, 6)
- (3, 5)
- (4, 4)
- (5, 3)
- (6, 2)

This gives us a total of 5 favorable outcomes.

3. **Calculate the probability**: The probability of the sum being 8 is given by the ratio of favorable outcomes to total outcomes:
\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{5}{36}
\]

So, the probability that the sum of the two cubes equals 8 is \( \frac{5}{36} \).