Relative And Expected Frequencies
8.2 Relative and Expected Frequencies – Cheat Sheet
1. Relative frequency as an estimate of probability
- Relative frequency = (Number of times event occurs) / (Total number of trials)
- P(A) ≈ relative frequency when number of trials is large
- Used when theoretical probability is not known or when based on experimental data
2. Expected frequency formula
Expected frequency = Probability × Total number of trials
E = P(A) × N
Example:
If P(A) = 0.4 and there are N = 200 trials,
E = 0.4 × 200 = 80
3. Key terms
- Fair: All outcomes are equally likely (e.g., an unbiased coin)
- Biased: Some outcomes are more likely than others due to unfairness in design or conditions
- Random: Outcomes occur without any predictable pattern
4. Examples
| Trial Number | Outcome | Tally | Frequency | Relative Frequency |
|---|---|---|---|---|
| 1–10 | Red | |||
| 1–10 | Blue | |||
| 1–10 | Green |
If repeated over 1000 trials, relative frequencies get closer to actual probabilities.