Skill: Describe simple probability using fractions

Probability tells how likely an event is to happen.

For equally likely outcomes, use the rule

$$\text{Probability}=\frac{\text{number of favorable outcomes}}{\text{number of all possible outcomes}}.$$

• Favorable outcomes are the outcomes that make the event happen.
• All possible outcomes are every outcome that could happen.

Example

What is the probability of rolling a number greater than $4$ on a fair six-sided die?

Step 1: List all possible outcomes.

A die can show

$$1,2,3,4,5,6$$

There are $6$ possible outcomes.

Step 2: Find the favorable outcomes.

The numbers greater than $4$ are

$$5,6$$

There are $2$ favorable outcomes.

Step 3: Write the probability as a fraction.

$$P(\text{number greater than }4)=\frac{2}{6}$$

Step 4: Simplify if possible.

Both $2$ and $6$ can be divided by $2$:

$$\frac{2}{6}=\frac{1}{3}$$

So, the probability is

$$\boxed{\frac{1}{3}}.$$

This means that $1$ out of every $3$ equally likely outcomes is favorable. A probability is always between $0$ and $1$: $0$ means impossible, and $1$ means certain.