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 plus Start Fraction 2 over 36 End Fraction 636 ⋅236 Start Fraction 6 over 36 End Fraction times Start Fraction 2 over 36 End Fraction 536 ⋅236 Start Fraction 5 over 36 End Fraction times Start Fraction 2 over 36 End Fraction 636 +236

Answer 1

To determine the probability of rolling two number cubes (dice) and getting a sum of 6 or 11, we need to consider the possible outcomes for each sum.

1. **Finding the probability of getting a sum of 6:**
The pairs that result in a sum of 6 are:
- (1, 5)
- (2, 4)
- (3, 3)
- (4, 2)
- (5, 1)

There are 5 outcomes that yield a sum of 6.

2. **Finding the probability of getting a sum of 11:**
The pairs that result in a sum of 11 are:
- (5, 6)
- (6, 5)

There are 2 outcomes that yield a sum of 11.

3. **Total outcomes:**
When rolling two dice, there are a total of 6 sides on the first die and 6 sides on the second die, which gives us \(6 \times 6 = 36\) possible outcomes.

4. **Calculating the probabilities:**
- The probability of getting a sum of 6 is \( \frac{5}{36} \).
- The probability of getting a sum of 11 is \( \frac{2}{36} \).

5. **Combining the probabilities:**
Since the events are mutually exclusive (you can't roll a sum of 6 and 11 at the same time), we can add the probabilities:
\[
P(6 \text{ or } 11) = P(6) + P(11) = \frac{5}{36} + \frac{2}{36} = \frac{7}{36}
\]

Based on this information, the correct calculation for finding the probability of rolling two dice and getting a sum of 6 or 11 is represented by:
\[
\frac{5}{36} + \frac{2}{36}
\]

Thus, the first option:
\[
\frac{5}{36} + \frac{2}{36}
\]
is the correct response.