Lesson 3: Understand Experimental Probability

Property

When the probability of an event is known, or can be determined through analysis where all outcomes are equally likely, the theoretical probability is:

Examples

• The theoretical probability of rolling a 2 on a six-sided die is $\frac{1}{6}$. If you roll it 12 times and get a 2 three times, the experimental probability is $\frac{3}{12}$ or $\frac{1}{4}$.
• A bag has 4 red and 6 blue marbles. The theoretical probability of drawing red is $\frac{4}{10} = \frac{2}{5}$. After drawing and replacing 20 times, you draw red 9 times. The experimental probability is $\frac{9}{20}$.
• A spinner has 4 equal sections. The theoretical probability of landing on 'A' is $\frac{1}{4}$. After 60 spins, it lands on 'A' 12 times. The experimental probability is $\frac{12}{60} = \frac{1}{5}$.

Explanation

Theoretical probability is what should happen based on pure math, like a $\frac{1}{2}$ chance of heads. Experimental probability is what actually happens when you run the experiment, like getting 47 heads in 100 flips.

Property

To predict future outcomes using experimental probability:
Expected number of occurrences = $P(\text{event}) \times \text{number of future trials}$, where $P(\text{event})$ is the experimental probability from past trials.

Examples