How is a frequency tree different from a probability tree diagram?

Frequency trees and two-way tables

Frequency trees and two-way tables sort a group into categories. Probabilities then come straight from the counts.

GCSE · 1MA1 · P1, P6, P9
International GCSE · 4MA1 · 6.1, 6.3
About 15 minutes

Frequency trees

A frequency tree shows how a total splits up, branch by branch. Unlike a probability tree, it shows numbers of people, not probabilities.
80 students: 35 walk to school and 45 do not.
Of the walkers, 7 were late and 28 were on time. Of the others, 9 were late and 36 were on time.
Each pair of branches adds up to the number before it.

Two-way tables

Rows and columns both add up to the totals.
	Late	On time	Total
Walk	7	28	35
Other	9	36	45
Total	16	64	80

Probabilities from the counts

P(late) = 1680 = 15
P(walks and late) = 780 = 780
Given a student walks, P(late) = 735 = 15: only look at the walk row.

Worked example

Of 80 students, 35 walk. 7 walkers and 9 others were late. How many students who do not walk were on time?

Students who do not walk: 80 − 35 = 45
On time: 45 − 9 = 36

Answer: 36

Key idea

Branches or rows must add up to their totals. Probability = count ÷ total of the group you are choosing from.

Quick check

Try two quick questions

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Extra practice

2 more questions

Try each one, then tap to check.

Of 120 students, 22 have a packed lunch. How many do not have one?
Show the answer
Answer: 98
120 − 22 = 98.
Of the 54 students who do not walk, 12 were late. How many were on time?
Show the answer
Answer: 42
54 − 12 = 42.

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Sources and references

Checked by the GCSE-ready editorial team, 17 October 2026. Last updated 2 October 2026. Spotted a mistake? Tell us and we will fix it.