Year 7 - Probability - Free practice

Year 7 Probability Worksheets & Practice Tests

Sample spaces, single-stage experiments, relative frequency.

Quick answer

How do you find the probability of an outcome in Year 7?

List the sample space (all possible outcomes), then write the probability as a fraction: favourable outcomes divided by total outcomes. For example, rolling a 4 on a normal die has probability 1/6 because there is 1 favourable outcome out of 6 equally likely outcomes. Probabilities can also be written as decimals or percentages.

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 7 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 7 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 · Listing the sample space and assigning probabilities
A standard six-sided die has faces numbered 1 to 6. List the sample space for one roll of the die, then find the probability of rolling a number greater than 4. Write your answer as a fraction, a decimal and a percentage.
Show worked solution
Key idea: The sample space is the list of all possible outcomes. Probability = $\dfrac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$
1. List the sample space: $\{1, 2, 3, 4, 5, 6\}$ . There are 6 equally likely outcomes.
2. Identify the favourable outcomes (greater than 4): $\{5, 6\}$ . There are 2 favourable outcomes.
3. Write the probability as a fraction: $P(\text{greater than 4}) = \frac{2}{6} = \frac{1}{3}$
4. Convert to a decimal: $\frac{1}{3} \approx 0.\overline{3}$
5. Convert to a percentage: $\frac{1}{3} \times 100 \approx 33.3\%$
Answer: $\dfrac{1}{3}$ , approximately $0.\overline{3}$ , approximately $33.3\%$
Example 2 · Complementary events
A bag contains 3 red marbles, 5 blue marbles and 2 yellow marbles. One marble is drawn at random. Find the probability that the marble is NOT blue.
Show worked solution
Key idea: Complementary events cover all outcomes that are not the chosen event. $P(\text{not } A) = 1 - P(A)$
1. Find the total number of marbles: $3 + 5 + 2 = 10$ .
2. Find $P(\text{blue}) = \dfrac{5}{10} = \dfrac{1}{2}$ .
3. Use the complement rule: $P(\text{not blue}) = 1 - \frac{1}{2} = \frac{1}{2}$
4. Check by listing non-blue marbles: $3 + 2 = 5$ marbles, so $P(\text{not blue}) = \dfrac{5}{10} = \dfrac{1}{2}$ . ✓
Answer: $\dfrac{1}{2}$
Example 3 · Comparing theoretical and experimental probability
Mia spins a fair four-sided spinner with equal sections labelled 1, 2, 3 and 4. She records her results over 40 spins and lands on 3 a total of 14 times. What is the theoretical probability of landing on 3? What is the experimental probability of landing on 3 based on Mia's results? By how many percentage points do these two probabilities differ? Round to one decimal place.
Show worked solution
Key idea: Theoretical probability uses equally likely outcomes; experimental probability uses actual results. Experimental probability $= \dfrac{\text{number of times the outcome occurred}}{\text{total number of trials}}$
1. Find the theoretical probability. There are 4 equally likely outcomes and one favourable outcome: $P(3) = \frac{1}{4} = 0.25 = 25\%$
2. Find the experimental probability using Mia's results: $P(\text{3 from experiment}) = \frac{14}{40} = \frac{7}{20} = 0.35 = 35\%$
3. Find the difference in percentage points: $35\% - 25\% = 10\%$
4. The experimental probability is 10 percentage points higher than the theoretical probability. This is expected because experiments with a small number of trials often differ from the theoretical value.
Answer: Theoretical probability: $25\%$ . Experimental probability: $35\%$ . Difference: $10$ percentage points.

Common mistakes

Where students usually lose marks

Forgetting to simplify the probability fraction

$P(\text{blue}) = \dfrac{5}{10}$ left unsimplified, or treated as a different answer to $\dfrac{1}{2}$

Always simplify probability fractions to lowest terms. Divide both the numerator and denominator by their highest common factor. $\dfrac{5}{10} = \dfrac{1}{2}$ are the same probability written differently.

Using the wrong total in the denominator

A bag has 3 red, 5 blue and 2 yellow marbles. $P(\text{red}) = \dfrac{3}{5}$ (using only blue as the total)

The denominator must always be the total number of outcomes in the sample space, not just one group. Add all groups together first: $3 + 5 + 2 = 10$ , so $P(\text{red}) = \dfrac{3}{10}$ .

Subtracting from 100 instead of 1 for the complement

$P(\text{not blue}) = 100 - \dfrac{1}{2} = 99.5$

The complement rule is $P(\text{not } A) = 1 - P(A)$ . If your probability is a fraction or decimal, subtract from 1. Only subtract from 100 if both probabilities are already expressed as percentages.

Confusing theoretical and experimental probability

Claiming that because $P(\text{heads}) = \dfrac{1}{2}$ , flipping a coin 10 times must give exactly 5 heads

Theoretical probability tells you what to expect on average over many trials, not what will happen every time. Experimental results vary, especially with a small number of trials, and experimental probability gets closer to theoretical probability as the number of trials increases.

Try one yourself

Your turn

A spinner is divided into 8 equal sections numbered 1 to 8. What is the probability of spinning a number greater than 5? Give your answer as a fraction.

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

Probability in Year 7 is mostly about listing all possible outcomes and assigning fractions to them. These worksheets keep the questions concrete - coins, dice, spinners, cards - while making sure your student handles the language ("equally likely", "impossible", "certain") correctly.

What's covered

Sub-skills your student will practise

✓Listing the sample space for a single-stage experiment
✓Assigning probabilities as fractions, decimals or percentages
✓Probability of complementary events
✓Relative frequency from experimental data
✓Comparing theoretical and experimental probabilities

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 kind of probability questions does Year 7 cover?

Single-stage experiments - one coin flip, one die roll, one spinner, one card drawn from a pack. Two-stage experiments (which need tree diagrams or two-way tables) arrive in Year 8.

How should probabilities be written?

Year 7 accepts fractions, decimals, or percentages, but the cleanest format is usually a fraction in simplest form. For 'pick a heart from a deck', 13/52 = 1/4 is the preferred form.

What does 'complementary event' mean?

The probability that an event doesn't happen. If P(rain) = 0.3, then P(no rain) = 0.7. Complementary probabilities always add to 1.

What's the difference between theoretical and experimental probability?

Theoretical probability is what the maths says should happen (P(heads) = 1/2). Experimental probability is what actually happened in a real trial (heads came up 47 times in 100 flips = 0.47). They get closer together as the number of trials increases.

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.