You roll two fair six-sided dice. What is the probability of getting a sum of 7?


To find the probability of rolling a sum of 7 with two six-sided dice, we follow these steps:

### Step 1: Determine the total number of possible outcomes.
Each die has 6 sides, so the total number of outcomes when rolling two dice is:
\[
6 \times 6 = 36
\]

### Step 2: Determine the favorable outcomes for a sum of 7.
We list all the pairs of dice that sum to 7:
- (1, 6)
- (2, 5)
- (3, 4)
- (4, 3)
- (5, 2)
- (6, 1)

There are 6 favorable outcomes.

### Step 3: Calculate the probability.
The probability is the number of favorable outcomes divided by the total number of possible outcomes:
\[
\frac{6}{36} = \frac{1}{6}
\]

Thus, the probability of getting a sum of 7 is \( \frac{1}{6} \).

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### Related Questions:
1. What is the probability of rolling a sum of 8 with two dice?
2. How many possible outcomes give a sum greater than 9 with two dice?
3. What is the probability of rolling a sum of 5 with two dice?
4. How does the probability change if you use an eight-sided die instead of a six-sided one?
5. What is the probability of rolling doubles (e.g., (1,1), (2,2)) with two dice?

#### Tip: When rolling two dice, the most likely sum is 7 because it has the most combinations that lead to this result!

You roll two fair six-sided dice. What is the probability of getting a sum of 7?

Discover how to calculate the probability of rolling a sum of 7 with two fair six-sided dice. This problem covers essential probability concepts and demonstrates the step-by-step method to find the probability by analyzing favorable outcomes. Ideal for students in Grades 6-8.

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