Relative frequency and expected frequency
Relative frequency
- When outcomes are not equally likely, run an experiment:
$$\text{relative frequency} = \frac{\text{times it happened}}{\text{total trials}}$$
- More trials → a better estimate. A fair object gives equal chances; one with bias does not.
Practice
Relative frequency is calculated as:
Relative frequency = successes ÷ number of trials.
Expected frequency
- How many times you expect an event in $n$ trials:
$$\text{expected frequency} = \text{P}(\text{event}) \times n$$
- Worked example: $\text{P}(\text{six}) = \tfrac16$, so in $300$ rolls you expect $\tfrac16 \times 300 = 50$ sixes.
Practice
The probability of rolling a six is 1/6. How many sixes are expected in 300 rolls?
(1/6) × 300 = 50.
Practice
An event has probability 0.2. How many times is it expected in 50 trials?
0.2 × 50 = 10.
You've got it
Key idea
- relative frequency $= \dfrac{\text{times happened}}{\text{total trials}}$ — an estimate that improves with more trials
- expected frequency $= \text{P}(\text{event}) \times n$
- $\tfrac16 \times 300 = 50$ expected sixes