📊 Getting Real with Relative Frequency!

Ever wondered how likely an event really is? Relative frequency gives us a **practical estimate** of probability by looking at real data instead of theory. For O Level exams, mastering this idea helps you tackle questions on experimental probability confidently.

What is Relative Frequency?

Relative frequency is the ratio of the number of times an event occurs to the total number of trials. In symbols:

\text{Relative Frequency} = \frac{\text{Number of Successes}}{\text{Total Trials}}.

Because it is based on **actual results**, it can differ from the theoretical probability, especially when the number of trials is small.

As the number of trials increases, relative frequency tends to get closer to the theoretical probability (Law of Large Numbers).
It is always between $0$ and $1$ , or $0\%$ and $100\%$ .

Worked Example: Rolling a Dice

Problem: A fair six-sided die is rolled 60 times. The number "6" appears 12 times. Find the relative frequency of rolling a six and comment on how it compares with the theoretical probability.

Step 1: Identify the figures:
$\text{Successes} = 12, \; \text{Trials} = 60.$
Step 2: Calculate relative frequency:
$\text{Relative Frequency} = \frac{12}{60} = 0.2.$
Step 3: Compare with theory: The theoretical probability of rolling a six is $\frac{1}{6} \approx 0.167$ . Our experimental value $0.2$ is close but slightly higher; with more rolls, it should get closer to $0.167$ .

Practice collecting data from simple experiments—coin tosses, dice rolls, or survey responses—and compute their relative frequencies. The more you try, the sharper your intuition for probability becomes. Keep experimenting and stay **exam-ready**!