Recording outcomes — tables and frequency trees
Frequency trees and two-way tables appear on every WJEC Unit 2 paper at Foundation and Intermediate, and feature in Higher conditional-probability problems too. The skill is systematic counting: every outcome appears once, totals reconcile.
Frequency tables
Records how often each outcome occurs.
| Score on dice | Frequency |
|---|---|
| 1 | 4 |
| 2 | 6 |
| 3 | 5 |
| 4 | 7 |
| 5 | 5 |
| 6 | 3 |
| Total | 30 |
Always include the total row and check it sums correctly.
Frequency trees (WJEC style)
Branching boxes (not probability trees with fractions). The left split is by one category (e.g. boys/girls), the right split by another (e.g. passed/failed).
Example: 80 students. 35 are boys. 12 of the boys passed. 50 passed in total.
- Boys: 35 → Pass = 12, Fail = 23.
- Girls: 80 − 35 = 45 → Pass = 50 − 12 = 38, Fail = 45 − 38 = 7.
- Check: 12 + 23 + 38 + 7 = 80. ✓
A standard WJEC question worth 3 marks asks you to "complete the frequency tree" and then 2 marks for "find the probability that a randomly chosen student is a girl who failed" — answer 7/80.
Two-way tables
Two categorical variables; cells hold frequencies; row totals + column totals + grand total.
| Likes maths | Dislikes maths | Total | |
|---|---|---|---|
| Year 9 | 18 | 12 | 30 |
| Year 10 | 22 | 8 | 30 |
| Total | 40 | 20 | 60 |
Probability from frequency
P(event) = frequency of event ÷ grand total.
P(Year 10 likes maths) = 22/60 = 11/30.
For conditional probability, divide by the row/column total: P(likes maths | Year 10) = 22/30 = 11/15.
WJEC exam tip
Fill in given values first, then deduce the remaining cells using row/column totals. The M1 method mark is for clearly subtracting from a total to find an unknown cell — show this working in pen.
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