To calculate the probability $P(D)$, where $D$ is the event of getting a sum of 11 when rolling two dice, we need to determine the following:

Step 1: Total Possible Outcomes

When rolling two six-sided dice, each die has 6 possible outcomes. Thus, the total number of possible outcomes when rolling two dice is: $6 \times 6 = 36$ These are all the possible combinations of outcomes from the two dice.

Step 2: Outcomes that Sum to 11

Next, we need to identify the combinations of numbers on the two dice that add up to 11. The pairs of numbers are:

• (5, 6)
• (6, 5)

There are 2 favorable outcomes where the sum of the dice is 11.

Step 3: Calculating Probability

The probability $P(D)$ is the ratio of favorable outcomes to total possible outcomes: $P(D) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{2}{36} = \frac{1}{18}$

So, the probability of the sum of the dice being 11 is $\frac{1}{18}$.

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Would you like further clarification on this? Let me know if you have any more questions.

Here are 5 related questions for you to explore:

1. What is the probability of getting a sum of 7 when rolling two dice?
2. How many ways can you get a sum of 12 with two dice?
3. What is the probability of rolling a sum less than or equal to 4 with two dice?
4. What is the probability of rolling a sum that is a multiple of 3?
5. If the first die shows a 3, what is the probability that the sum of the dice is 11?

Tip: When calculating probabilities for dice rolls, always start by identifying all possible outcomes and then count the favorable ones.