Year 9 - Probability - Free practice
Year 9 Probability Worksheets & Practice Tests
With/without replacement, multi-step events, relative frequency.
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10 questions — 4 Foundation, 4 Standard, 2 Extension — with full worked solutions, calibrated to the Victorian Curriculum.
About this worksheet
Why we built it
Year 9 probability mostly distinguishes "with replacement" from "without replacement" in two-step experiments. These worksheets give your student varied tree diagrams, tables and worded scenarios so the rule for adjusting the second draw becomes automatic.
What's covered
Sub-skills your student will practise
- ✓Tree diagrams with and without replacement
- ✓Tables for two-step experiments
- ✓And vs or probability questions
- ✓Calculating relative frequency from data
- ✓Designing simulations to estimate probabilities
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Frequently asked
Questions parents ask about probability
What does 'two-step experiment' mean?
A probability experiment with two stages - flip a coin then roll a die, or pick two cards in sequence. Year 9 introduces tree diagrams for these, with branches for each stage.
What's 'with replacement' vs 'without replacement'?
With replacement: the first item is returned before the second draw, so each stage's probability stays the same. Without replacement: the first item is kept, so the second-stage probability shifts.
How does Year 9 handle 'and' / 'or' probabilities?
P(A and B) = P(A) x P(B) for independent events. P(A or B) = P(A) + P(B) - P(A and B) using the inclusion-exclusion rule. Year 9 introduces both formally.
What's relative frequency?
The proportion of times an outcome actually occurred in a real experiment. Tossing a coin 100 times and getting 47 heads gives a relative frequency of 47/100 = 0.47. Long-run relative frequencies approach theoretical probabilities.
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