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Year 7 · Geometric Reasoning

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Year 10 · Probability

Sample Spaces

Twenty practice questions in the format of the "strict luggage provisions" question on your test — a real-world scenario, a few decisions to make, and one or two restrictions on how the choices combine.

For every question you'll be asked to:

How to enter your answers

For probability questions, type either form — fraction or decimal:

For "how many outcomes?" questions, type a whole number.

Scaffolded then independent

Set 1 walks you through the method on a worked example, then helps you with diminishing scaffolding through Q2–5. From Q6 onward you're on your own — but the same five-step method works on every problem.

Bring scrap paper. Drawing a tree diagram or listing combinations on paper will make every part faster — that's still the most reliable way to handle these problems on a real test.
Sample Spaces · Probability  ·  20 questions, 60 graded answers
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Twenty Sample Spaces

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You've worked through twenty sample-space problems with restrictions. The pattern is now in your hands — bring it to the test.

The five-step method (your tree-diagram routine):
1. Identify the two main categories and the common decision.
2. List every combination — categories × common options.
3. Cross out forbidden combinations (apply each restriction).
4. Count what remains — that's your sample space.
5. Probability = favourable outcomes ÷ total. For conditional, restrict the sample space to outcomes where the "given" condition is true.