Year 9 - Probability - Free practice
Year 9 Probability Worksheets & Practice Tests
With/without replacement, multi-step events, relative frequency.
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Six questions across Foundation, Standard and Extension, with full worked solutions, calibrated to the Victorian Curriculum.
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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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From our families
Parents on the practice questions.
“Tuterly has been exactly what we needed since Tom started secondary school. Once the topic tests began, he was struggling to keep up. Now he has unlimited practice, all matched to what his class is actually covering, and his Maths results have improved noticeably.”
Rebecca M.
Year 8 · Maths
“My daughter used to leave revision until the night before. Having a platform she can dip into for fifteen minutes after dinner has completely changed that. She's calmer going into assessments, and honestly, so am I.”
Priya S.
Year 9 · Maths
“I like that I can just keep doing questions until it clicks. If I get something wrong, it shows me why, and then gives me another one like it.”
Ella, student
Year 10 · Maths
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.
Want a real plan for the term?
Worksheets are great for repetition. A Tuterly tutor can spot the specific moves your student keeps getting wrong and fix them in one or two sessions.
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