Year 8 - Probability - Free practice

Year 8 Probability Worksheets & Practice Tests

Tree diagrams, two-way tables, Venn diagrams.

Quick answer

How do you find all possible outcomes for two events in probability?

Use a tree diagram or two-way table to list every possible outcome combination. A tree diagram branches at each stage, while a two-way table arranges outcomes in rows and columns. For example, flipping a coin then rolling a die gives 2 × 6 = 12 outcomes, each shown as a branch pair or a cell in the table.

Generate a free maths worksheet

Six questions across Foundation, Standard and Extension, with full worked solutions, written to the Australian Curriculum.

Want more than a worksheet?

Practice built from mistakes.

A worksheet on Year 8 probability is a good start. Tuterly goes further: it turns any question students get wrong into fresh practice, at the right level, on what’s likely to be in the next test or exam.

~90% of Bayside Academics students using it weekly improved their test marks

Of the Bayside Academics students who used Tuterly at least once a week, about 90% improved their school test marks.

Based on the actual school test marks of 100+ Bayside Academics students (in person and online) in Years 7 to 10, before and after using Tuterly at least once a week. How we measured this

Free worksheet Tuterly

The questionsFree worksheetThe same questions for every student on this topic.TuterlyWritten from the questions they got wrong in homework and school tests, at their level.

How manyFree worksheetOne sheet at a time.TuterlyAs many fresh questions as they need, each one different, never just the numbers swapped.*

Before a testFree worksheetPick a topic and hope it’s the right one.TuterlyA practice test covering every part of the topic. Upload the term planner and it focuses on what’s coming up.

MarkingFree worksheetCheck the answer key yourself.TuterlyMarked as they go, with the exact step that went wrong explained.

ProgressFree worksheetNothing is saved.TuterlyEvery question tracked until it’s mastered, and a weekly review for parents.

For Years 7 to 10: $8.99 a week or $29.99 a month at the launch price (from 1 April 2027, $17.99 a week or $59.99 a month), with a 7-day free trial on the monthly plan only. Better marks in 6 months, or your money back.

Or try it free now on one of their questions →

Coming soon on iPhone. Android soon after.

Free to download · 7-day free trial on monthly · Years 7 to 10 maths · On iPhone. Android coming soon

* With a subscription. Fair use applies: up to 80 snapped questions and 120 new practice questions a day per student.

Worked examples

Year 8 probability: worked examples

Three examples, from a standard question to a worded problem. Have a go at each one before you open the solution.

Example 1 · Tree diagram for two-stage experiment
A bag contains one red marble (R) and one blue marble (B). A marble is drawn, its colour is recorded, and it is put back. A second marble is then drawn. List all possible outcomes using a tree diagram and find the probability of getting two red marbles.
Show worked solution
Key idea: Draw a tree diagram by listing every branch for the first draw, then every branch for the second draw from each first-draw branch. Because the marble is replaced, the bag is the same for both draws.
1. First draw has two branches: R and B.
2. From each branch, the second draw also has two branches: R and B. The complete sample space is: RR, RB, BR, BB, 4 equally likely outcomes.
3. Only one outcome is two red marbles: RR.
4. $P(\text{RR}) = \frac{1}{4}$
Answer: $P(\text{two red marbles}) = \dfrac{1}{4}$
Example 2 · Two-way table without replacement
A bag contains 3 cards numbered 1, 2 and 3. One card is drawn and not replaced, then a second card is drawn. Construct a two-way table of all possible outcomes and find the probability that the sum of the two cards is greater than 4.
Show worked solution
Key idea: In a two-way table for sampling without replacement, a card cannot appear twice in the same draw, so outcomes where both draws give the same number are impossible and are crossed out.
1. Set up a table with the first draw as rows (1, 2, 3) and the second draw as columns (1, 2, 3).
First \ Second 1 2 3
1 , (1,2) (1,3)
2 (2,1) , (2,3)
3 (3,1) (3,2) ,
1. There are 6 equally likely outcomes.
2. Find the sums: $(1,2)\to 3$ , $(1,3)\to 4$ , $(2,1)\to 3$ , $(2,3)\to 5$ , $(3,1)\to 4$ , $(3,2)\to 5$ .
3. Outcomes with sum $> 4$ : $(2,3)$ and $(3,2)$ , that is 2 outcomes.
4. $P(\text{sum} > 4) = \frac{2}{6} = \frac{1}{3}$
Answer: $P(\text{sum} > 4) = \dfrac{1}{3}$
Example 3 · Venn diagram and probability, real-life context
In a class of 30 students, 18 students play football, 14 students play basketball, and 6 students play both sports. A student is chosen at random. Find the probability that the student plays neither football nor basketball.
Show worked solution
Key idea: Draw a Venn diagram with two overlapping circles, one for football (F) and one for basketball (B), inside a rectangle representing all 30 students. Place the overlap count first, then fill in the rest of each circle.
1. The overlap (both sports) contains 6 students.
2. Football only: $18 - 6 = 12$ students. Basketball only: $14 - 6 = 8$ students.
3. Total accounted for inside the circles: $12 + 6 + 8 = 26$ students.
4. Students outside both circles (neither sport): $30 - 26 = 4$ students.
5. $P(\text{neither}) = \frac{4}{30} = \frac{2}{15}$
Answer: $P(\text{neither football nor basketball}) = \dfrac{2}{15}$

First \ Second	1	2	3
1	,	(1,2)	(1,3)
2	(2,1)	,	(2,3)
3	(3,1)	(3,2)	,

Common mistakes

Where students usually lose marks

Forgetting to remove the first item when sampling without replacement

Drawing card 1 then card 1 again is listed as a valid outcome.

When sampling without replacement, the first item is gone before the second draw. Cross out the diagonal of a two-way table (or remove the used branch) so the same card cannot appear twice.

Counting the overlap twice in a Venn diagram

$18 + 14 = 32$ students play at least one sport in a class of 30.

Students in both circles are counted once in each total, so they must be subtracted once: $18 + 14 - 6 = 26$ . Always subtract the overlap when adding two groups.

Listing fewer branches in later stages of a tree diagram

After drawing a red marble, only one branch (blue) is drawn for the second draw.

Every outcome from the first stage must lead to a full set of branches for the second stage. If there are 2 options at stage 1, each must show all available options at stage 2.

Confusing P(A and B) with P(A or B)

$P(\text{football and basketball}) = \frac{18}{30} + \frac{14}{30} = \frac{32}{30}$

$P(A \text{ and } B)$ means both events happen at the same time, it comes from the overlap only. Use the overlapping region of the Venn diagram or the branch where both outcomes occur in a tree diagram.

Try one yourself

Your turn

A bag contains one red ( $R$ ) marble and one blue ( $B$ ) marble. A marble is drawn, its colour recorded, and it is returned to the bag. A second marble is then drawn. Using the equally likely outcomes, what is the probability of drawing two marbles of the same colour? Give your answer as a fraction in the form $p/q$ , enter the value as a decimal.

Got a different probability question wrong? Upload it to Tuterly and get the worked solution and a fresh one to practise, free.

About this worksheet

Why we built it

Year 8 probability adds two-event experiments - which means tree diagrams, two-way tables and Venn diagrams enter the picture. These worksheets give your student practice in each representation so they can pick whichever is fastest for the question in front of them.

What's covered

Sub-skills your student will practise

✓Tree diagrams for two-stage experiments
✓Two-way tables (with-replacement and without-replacement)
✓Venn diagrams for two events
✓Complementary events
✓Calculating P(A and B) from a tree or table

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

Verified parent

Frequently asked

Questions parents ask about probability

What's a tree diagram used for?

Mapping out all possible outcomes of a multi-stage event. Each branch is one possible outcome at one stage. Year 8 introduces two-stage tree diagrams - three coin flips, picking two marbles, etc.

What's the difference between 'with' and 'without' replacement?

With replacement: the first item is put back before the second is drawn, so each draw has the same probability. Without replacement: the first item stays out, so the second draw's probability changes. This catches a lot of students out.

When do students use a two-way table vs a tree diagram?

Two-way tables work well when you already have category totals. Tree diagrams are better when probabilities differ at each stage. Venn diagrams suit problems involving 'and / or' overlap between events.

What's a complementary event in Year 8?

The opposite of an event - if A is 'roll a 6', then 'not A' is 'roll 1, 2, 3, 4, or 5'. P(A) + P(not A) = 1 always. This is one of the most-used probability shortcuts in Year 8 problems.

Better maths marks start with the next wrong answer.

Tuterly turns every missed maths question into practice tailored towards the student, not just a generic worksheet.