Skill: Find probabilities from dice

For a probability with dice, use

$$\text{Probability}=\frac{\text{number of favorable outcomes}}{\text{total number of equally likely outcomes}}.$$

Example: What is the probability that the sum of two fair six-sided dice is $7$?

Step 1: Count the total outcomes.
Each die has $6$ possible results. For two dice, the outcomes are ordered pairs, such as $((2,5))$, meaning the first die shows $2$ and the second shows $5$.

So there are

$$6 \times 6=36$$

equally likely outcomes.

Step 2: Find the favorable outcomes.
The pairs that add to $7$ are

$$(1,6),\ (2,5),\ (3,4),\ (4,3),\ (5,2),\ (6,1).$$

There are $6$ favorable outcomes.

Step 3: Write and simplify the probability.

$$P(\text{sum of }7)=\frac{6}{36}=\frac{1}{6}.$$

As a decimal and percent:

$$\frac{1}{6}\approx 0.167\approx 16.7\%.$$

So, the probability of rolling a sum of $7$ is

$$\boxed{\frac{1}{6}\text{, or about }16.7\%}.$$

Remember: With two dice, there are $(36)$ equally likely ordered pairs. The sums themselves are not equally likely because some sums can be made in more ways than others.