Relative & Expected Frequency

What Is Relative Frequency?

Relative frequency is a way of estimating the probability of an event by performing an experiment and using the results.

If you repeat an experiment multiple times, you can calculate: $$\text{Relative Frequency} = \frac{\text{Number of times the event happens}}{\text{Total number of trials}}$$

This estimate becomes more accurate the more times the experiment is repeated.

Example

Aisha rolls a biased 6-sided die 60 times. It lands on a 6 twenty-four times.

Estimate the probability of the die landing on a 6.

Solution:

$\text{Relative Frequency} = \frac{24}{60} = \frac{2}{5}$

So, the estimated probability of rolling a 6 is $\frac{2}{5}$.

What Is Expected Frequency?

Expected frequency tells us how many times we would expect an event to occur, based on its probability and the number of trials.

To calculate expected frequency:

$$\text{Expected Frequency} = \text{Probability} \times \text{Number of Trials}$$

Example

A fair spinner has 4 equal sections: Red, Blue, Green, and Yellow.

(a) What is the probability of landing on Green?

(b) How many times would you expect to land on Green in 120 spins?

Solution:

(a) There are 4 equal sections, so: $P(\text{Green}) = \frac{1}{4}$

(b) Multiply the probability by the number of trials: $\text{Expected Frequency} = \frac{1}{4} \times 120 = 30$

We would expect 30 spins to land on Green.