Recording Probability Outcomes
Recording Probability Outcomes
Probability experiments generate outcomes that need to be recorded systematically. The tools at GCSE — tables, frequency trees, two-way tables and sample space diagrams — are all ways of organising outcome data so that probabilities can be calculated accurately.
Key Vocabulary
| Term | Meaning |
|---|---|
| Outcome | A single result of an experiment |
| Event | A set of one or more outcomes |
| Sample space | The set of all possible outcomes |
| Frequency | The number of times an outcome occurs |
| Relative frequency | Frequency ÷ total number of trials |
| Probability scale | 0 (impossible) to 1 (certain) |
Frequency Trees
A frequency tree records results of a two-stage experiment by branching. Each branch is labelled with the count (frequency), and counts at each level must sum to the total.
Two-Way Tables
Two-way tables organise data for two categorical variables simultaneously. Row totals and column totals must agree with the overall total.
The Probability Scale
All probabilities lie in the range \( 0 \leq P(A) \leq 1 \). Probabilities can be expressed as fractions, decimals or percentages — fractions are usually preferred in formal answers.
Key Takeaways
- Probability = favourable outcomes ÷ total possible outcomes (for equally likely outcomes).
- Relative frequency = frequency ÷ total trials (from experimental data).
- Frequency trees: branch counts must sum at each node.
- Two-way tables: row, column and grand totals must be consistent.
- All probabilities: \( 0\leq P\leq1 \). Impossible = 0, certain = 1.