Question

Which of the following shows the correct calculation for finding the probability of rolling two number cubes and getting a sum of 6 or 11?(1 point)
Responses

536 ⋅236
Start Fraction 5 over 36 End Fraction times Start Fraction 2 over 36 End Fraction

636 ⋅236
Start Fraction 6 over 36 End Fraction times Start Fraction 2 over 36 End Fraction

636 +236
Start Fraction 6 over 36 End Fraction plus Start Fraction 2 over 36 End Fraction

536 +236

Answer 1

To find the probability of rolling two number cubes (dice) and getting a sum of 6 or 11, we first need to calculate the probabilities of each of these sums separately and then combine them.

**Step 1: Calculate the total possible outcomes when rolling two dice.**
- There are \(6\) faces on each die, so the total number of outcomes when rolling two dice is \(6 \times 6 = 36\).

**Step 2: Determine the number of outcomes for each sum.**

- **Sum of 6:**
The combinations that give a sum of 6 are:
- (1, 5)
- (2, 4)
- (3, 3)
- (4, 2)
- (5, 1)

This gives us a total of **5 combinations** for a sum of 6. Therefore, the probability of a sum of 6 is:
\[
\frac{5}{36}
\]

- **Sum of 11:**
The combinations that give a sum of 11 are:
- (5, 6)
- (6, 5)

This gives us a total of **2 combinations** for a sum of 11. Therefore, the probability of a sum of 11 is:
\[
\frac{2}{36} = \frac{1}{18}
\]

**Step 3: Combine the probabilities for sums of 6 and 11.**
The total probability of getting a sum of 6 or 11 is the sum of the individual probabilities:
\[
P(6 \text{ or } 11) = P(6) + P(11) = \frac{5}{36} + \frac{2}{36} = \frac{7}{36}
\]

Now we evaluate the answer choices based on this calculation:
1. **\( \frac{5}{36} \cdot \frac{2}{36} \)** - This is a multiplication of probabilities, which is incorrect.
2. **\( \frac{6}{36} \cdot \frac{2}{36} \)** - This is also incorrect.
3. **\( \frac{6}{36} + \frac{2}{36} \)** - This is incorrect since \( \frac{6}{36} \) is not the correct probability for a sum of 6.
4. **\( \frac{5}{36} + \frac{2}{36} \)** - This matches our calculation for the sum probs, but this option is not listed correctly.

None of the options provided in the responses accurately reflect the addition of \( \frac{5}{36} + \frac{2}{36} \).

However, based on the closest patterns, if discussed in fundamentals, the correct calculation should be represented by:
**\( \frac{5}{36} + \frac{2}{36} \)**, which isn't explicitly there, but if you had to choose, the one that shows addition would be the most aligned: **\( \frac{6}{36} + \frac{2}{36} \)** if viewed simply as a structure.

So, choose accordingly based on the sum basics mentioned here.