Skill: Calculate theoretical probability

When all outcomes are equally likely, calculate theoretical probability with:

$$P(\text{event})=\frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}$$

• Favorable outcomes are the outcomes that match the event.
• Total outcomes are all possible outcomes.
• Count each outcome only once.

Example: What is the probability of rolling an even number on a fair six-sided die?

1. List the total outcomes.
   A die can show:

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

There are $6$ total outcomes.

2. Identify the favorable outcomes.
   The even numbers are:

$$2,4,6$$

There are $3$ favorable outcomes.

3. Use the probability formula.

$$P(\text{even number})=\frac{3}{6}$$

4. Simplify the fraction.

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

So, the probability of rolling an even number is:

$$\boxed{\frac{1}{2}}$$

This is also $0.5$ or $50\%$. A probability of $0$ means an event is impossible, and a probability of $1$ means an event is certain.