Question

What is the probability of getting a sum of 7 when rolling two six-sided dice?

Answer 1

To determine the probability of rolling a sum of 7 with two six-sided dice, we first need to calculate the total number of possible outcomes when rolling the dice.

When rolling two six-sided dice, each die can land on one of 6 faces. Thus, the total number of outcomes when rolling two dice is:

\[
6 \times 6 = 36
\]

Next, we need to find the number of favorable outcomes that result in a sum of 7. We can list the combinations that yield a sum of 7:

1. Die 1: 1, Die 2: 6 → (1, 6)
2. Die 1: 2, Die 2: 5 → (2, 5)
3. Die 1: 3, Die 2: 4 → (3, 4)
4. Die 1: 4, Die 2: 3 → (4, 3)
5. Die 1: 5, Die 2: 2 → (5, 2)
6. Die 1: 6, Die 2: 1 → (6, 1)

These are the combinations that give a sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). There are a total of 6 favorable outcomes.

Now, we can calculate the probability \( P \) of rolling a sum of 7:

\[
P(\text{sum of 7}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{6}{36}
\]

This fraction can be simplified:

\[
P(\text{sum of 7}) = \frac{1}{6}
\]

Thus, the probability of rolling a sum of 7 with two six-sided dice is

\[
\boxed{\frac{1}{6}}
\]