Experiments · Core / Foundation
A spinner landed on 4 in 36 of 120 spins. Find the relative frequency of a 4, and the expected number of 4s in 500 spins.
- Relative frequency = 36 ÷ 120 = 0.3
- Expected number = 0.3 × 500 = 150
Answer: 0.3 and 150
Probability, Venn diagrams & tree diagrams
Probability Lab
Mapped to Cambridge IGCSE 0580 C/E8.1–8.4 and C/E1.2 (sets) and GCSE P1–P9, with question types taken from recent papers: “complete the tree diagram”, “shade A ∩ B′ on the Venn diagram”, “two sweets are taken without replacement”, “given that the first counter is red…”. Answers are given as fractions, decimals or percentages, as the syllabus requires.
What students practise
- The probability scale, single events and P(not A); missing probabilities in a table
- Relative frequency, expected frequency, fair or biased
- Sample space diagrams for two events
- Set notation and Venn diagrams: completing, shading and counting (two sets at Core, three at Extended)
- Probabilities from Venn diagrams, including P(A ∩ B) and P(A ∪ B) at Extended
- Tree diagrams with replacement: multiply along, add between
- Without replacement: two and three picks, finding n (Extended / Higher)
- Conditional probability from grids, tables, Venn and tree diagrams (Extended / Higher)
How it works
Learn
20 lessons, each labelled with the exams it is for, with interactive models and worked examples.
Practise
Eight stations, fresh questions each visit, with hints that fade.
Challenge
Mixed questions from every station with a skill-by-skill report.
For teachers
Open Teacher options to choose Core / Foundation or Extended / Higher. Core limits are built in: with-replacement only and Venn diagrams with two sets. Nothing is uploaded: progress stays in each student's browser, so no accounts or data-protection paperwork are needed.
Which exams it covers
Every station is matched to the current specifications. Teacher options switch between Core/Foundation and Extended/Higher, and the Core limits from the 0580 syllabus are built in.
| Topic | GCSE (AQA, Edexcel) | Cambridge IGCSE 0580 |
|---|---|---|
| Probability scale, single events, P(not A) | P1, P2, P4 | C8.1 / E8.1 |
| Relative and expected frequency | P3, P5 | C8.2 / E8.2 |
| Sample space diagrams | P6, P7 | C8.3 / E8.3 |
| Sets, set notation and Venn diagrams | P6, P7 | C1.2 / E1.2 (two sets at Core) |
| Tree diagrams | P8 | C8.3 / E8.3 (Core: with replacement only) |
| Without replacement | P8 | E8.3 (Extended only) |
| Conditional probability | P9 (Higher only) | E8.4 (Extended only) |
Worked examples
Four examples of the kind of question the game generates, from Core/Foundation to Extended/Higher.
Tree Diagrams · Core / Foundation
A bag has 3 red and 5 blue counters. A counter is taken, replaced, and a second is taken. Find the probability that both are the same colour.
- P(red, red) = 3/8 × 3/8 = 9/64
- P(blue, blue) = 5/8 × 5/8 = 25/64
- Add: 9/64 + 25/64 = 34/64
Answer: 17/32
Without Replacement · Extended / Higher
A bag has 5 red and 3 blue sweets. Two are taken without replacement. Find the probability that they are different colours.
- P(red, blue) = 5/8 × 3/7 = 15/56
- P(blue, red) = 3/8 × 5/7 = 15/56
- Add: 30/56
Answer: 15/28
Conditional · Extended / Higher
In a class of 30, 15 study Biology, 12 study Art and 5 study both. A Biology student is chosen at random. Find the probability that they also study Art.
- Only the 15 Biology students count
- 5 of them also study Art
Answer: 5/15 = 1/3
Common mistakes the game targets
- Writing probability as a ratio. The syllabus says give probabilities as a fraction, decimal or percentage: 3/8, not 3 : 5 or “3 in 8”.
- Adding along the branches. Multiply along a path; add the paths you want.
- Keeping the same fractions without replacement. After one is taken, the total and possibly the top both go down by 1.
- Missing the outside of the Venn diagram. Students in neither set still belong in the rectangle, and still count in the total.
- Using the whole total for “given that”. In a conditional question the total shrinks to the group you were given.
Questions teachers and parents ask
Is the game free?
Yes. It is free to use, with no account, no adverts and no tracking. Progress is saved only in the student's own browser.
Which exams does it cover?
Cambridge IGCSE 0580 Core and Extended, and GCSE Foundation and Higher (AQA and Edexcel). Every lesson shows which exam and tier it is for.
Does it follow the Core limits?
Yes. At Core / Foundation level, tree diagrams are with replacement only and Venn diagrams have two sets, as the 0580 syllabus states. Without replacement, three-set Venn diagrams and conditional probability appear at Extended / Higher.
How do students type answers?
As a fraction, a decimal or a percentage, such as 3/8, 0.375 or 37.5%. Venn regions are shaded by tapping.
Are there printable worksheets to go with it?
Yes. The IGCSE 0580 Probability Paper 2 and Paper 4 packs, with exam-style tests and mark schemes, are on the Resources page.
Matching worksheet packs
Printable practice and exam-style tests on the same topic, with full worked solutions.
Probability
Probability — IGCSE 0580 Paper 2
Paper 2 (non-calculator) style practice and an exam-style test.
Free practice: Probability Lab
Probability
Probability — IGCSE 0580 Paper 4
Paper 4 (calculator) style practice and an exam-style test.
Free practice: Probability Lab
Need worksheets and lessons to go with the games?
Printable IGCSE and GCSE resources from Mathwright: worksheets, exam-style practice and full worked solutions.
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