Skill: Determine theoretical probability

Theoretical probability predicts how likely an event is by assuming all outcomes are equally likely.

Use the formula

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

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

1. List the possible outcomes.
   A six-sided die can land on

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

There are $6$ total possible outcomes.

2. Identify the favorable outcomes.
   The numbers greater than $4$ are

$$5 \text{ and } 6.$$

There are $2$ favorable outcomes.

3. Substitute into the formula.

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

4. Simplify and express the probability.

$$\frac{2}{6}=\frac{1}{3}=0.333\ldots\approx 33.3\%.$$

So, the theoretical probability is $\boxed{\frac{1}{3}}$, or about $\boxed{33.3\%}$.

This is a prediction based on equally likely outcomes. The results from actually rolling the die may not be exactly $33.3\%$, especially if you only roll it a small number of times.