5. what is the probability of rolling a sum that is not a 7 or an 11 with a pair of dice?

Explanation:

Step1: Find total number of outcomes

When rolling two dice, each die has 6 possible outcomes. So the total number of outcomes when rolling two dice is $6\times6 = 36$.

Step2: Find number of ways to get a sum of 7

The possible combinations for a sum of 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1), so there are 6 ways.

Step3: Find number of ways to get a sum of 11

The possible combinations for a sum of 11 are (5,6), (6,5), so there are 2 ways.

Step4: Find number of favorable outcomes

The number of ways to get a 7 or 11 is $6 + 2=8$. The number of ways to get a sum that is not 7 or 11 is $36-8 = 28$.

Step5: Calculate the probability

The probability $P$ is the number of favorable outcomes divided by the total number of outcomes. So $P=\frac{28}{36}=\frac{7}{9}$.

Answer:

$\frac{7}{9}$