Question

What is the probability of rolling a sum greater than 10 and a sum of 10 when rolling two number cubes?(1 point)
Responses

1144
Start Fraction 1 over 144 End Fraction

336
Start Fraction 3 over 36 End Fraction

13
Start Fraction 1 over 3 End Fraction

036
Start Fraction 0 over 36 End Fraction
Remaining Attempts : 3
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Answer 1

To determine the probabilities of rolling a sum greater than 10 and a sum of 10 when rolling two six-sided dice (number cubes), we first need to consider the total number of outcomes.

When rolling two dice, the total number of possible outcomes is:

\[
6 \times 6 = 36
\]

### Sum of 10
Next, we count the combinations that produce a sum of 10:

- (4, 6)
- (5, 5)
- (6, 4)

So, there are **3 combinations** that yield a sum of 10.

### Sum Greater than 10
Now, we count the combinations that produce a sum greater than 10. The possible sums greater than 10 when rolling two dice are 11 and 12.

- **Sum of 11:**
- (5, 6)
- (6, 5)

There are **2 combinations** that yield a sum of 11.

- **Sum of 12:**
- (6, 6)

There is **1 combination** that yields a sum of 12.

Adding these gives us the total combinations for sums greater than 10:

\[
2 + 1 = 3
\]

### Probabilities
Now we can calculate the probabilities.

1. **Probability of rolling a sum of 10:**

\[
P(\text{sum} = 10) = \frac{\text{number of ways to get 10}}{\text{total outcomes}} = \frac{3}{36} = \frac{1}{12}
\]

2. **Probability of rolling a sum greater than 10:**

\[
P(\text{sum} > 10) = \frac{\text{number of ways to get greater than 10}}{\text{total outcomes}} = \frac{3}{36} = \frac{1}{12}
\]

### Answer
The correct answer for the sums (10 or greater than 10) is:

- **Start Fraction 3 over 36 End Fraction** for the probability of rolling a sum greater than 10 or a sum of 10.

Since both probabilities yield **3 out of 36** combinations for each scenario, this is the answer that aligns with the options given.