Question

What is the probability of rolling a sum greater than 10 and a sum of 10 when rolling two number cubes?

Answer 1

To calculate the probabilities of rolling a sum greater than 10 and a sum of 10 with two number cubes (also known as dice), we need to examine the possible outcomes when rolling the dice.

1. **Total Outcomes**: When rolling two six-sided dice, the total number of outcomes is \(6 \times 6 = 36\).

2. **Sum of 10**: We need to count the pairs of rolls that give a sum of 10:
- Possible combinations:
- (4, 6)
- (5, 5)
- (6, 4)

The pairs that sum to 10 are:
- (4, 6)
- (5, 5)
- (6, 4)

Thus, there are 3 combinations that result in a sum of 10.

3. **Sum Greater than 10**: Now we determine the combinations that give sums greater than 10:
- Possible sums greater than 10 are 11 and 12.
- For sum of 11:
- (5, 6)
- (6, 5)

- For sum of 12:
- (6, 6)

Thus, there are 3 combinations that result in sums greater than 10.

4. **Calculating Probabilities**:
- Probability of rolling a sum of 10:
\[
P(\text{Sum of } 10) = \frac{\text{Number of ways to get 10}}{\text{Total outcomes}} = \frac{3}{36} = \frac{1}{12}
\]

- Probability of rolling a sum greater than 10:
\[
P(\text{Sum greater than } 10) = \frac{\text{Number of ways to get greater than 10}}{\text{Total outcomes}} = \frac{3}{36} = \frac{1}{12}
\]

So, the final probabilities are:
- The probability of rolling a sum of 10 is \(\frac{1}{12}\).
- The probability of rolling a sum greater than 10 is also \(\frac{1}{12}\).