Year 7 · Mathematics · Probability
Probability as numbers
Describe probabilities using fractions, decimals and percentages between 0 and 1, and compare the expected and observed results of repeated chance experiments.
Awaiting educator review. This material was drafted by our content team with AI assistance and is waiting for review by a qualified educator. Please check it suits your child before using it. Created 10 October 2026. How we review
These lessons were written around Australian Curriculum strands and matched to UK year groups by age (Year 1 is the year a child turns 6 in England). They are not mapped to the National Curriculum in England or the curricula of Scotland, Wales or Northern Ireland, so check them against your own plans.
Learning goals
Learners will
- Describe probabilities as numbers from 0 to 1.
- Write probabilities as fractions, decimals and percentages.
- Compare expected results with observed results from repeated chance experiments.
Success looks like
- I can place events on a probability scale from 0 (impossible) to 1 (certain).
- I can work out the probability of an outcome when all outcomes are equally likely, and write it as a fraction, decimal and percentage.
- I can calculate the expected number of results for many trials and compare it with what actually happened.
The big idea
We can describe chance using numbers on a probability scale from 0 to 1. An impossible event has a probability of 0. A certain event has a probability of 1. An event with an even chance, like a fair coin landing heads, has a probability of [frac 1/2], which is 0.5 or 50%.
When all outcomes are equally likely, the probability of an event is:
- the number of outcomes in the event, divided by the total number of possible outcomes.
For a standard die there are 6 equally likely outcomes. The probability of rolling a 4 is 16. The probability of rolling an even number (2, 4 or 6) is 36, which simplifies to 12.
Probabilities can be written as fractions, decimals or percentages. In a bag of 3 red, 2 blue and 5 green counters (10 counters in total), the probability of choosing red is 310 = 0.3 = 30%. Writing probabilities the same way makes them easy to compare: green is 510 = 0.5 = 50%, so green is more likely than red.
The probabilities of all the possible outcomes add up to 1. In the bag: 0.3 + 0.2 + 0.5 = 1.
We can use probability to find the expected frequency: multiply the probability by the number of trials. If a die is rolled 60 times, we expect each number about 16 × 60 = 10 times.
The observed frequency is what actually happens. If a coin lands heads 18 times in 40 flips, the observed fraction of heads is 1840 = 0.45 = 45%, which is close to the expected 50%. Results usually differ a little from what we expect, and the more trials we do, the closer the observed results tend to get to the probabilities.
Worked examples
Probabilities with a die
A standard die is rolled once. Find the probability of: (a) rolling a 5, (b) rolling a number less than 3, (c) rolling a 7.
- There are 6 equally likely outcomes: 1, 2, 3, 4, 5, 6.
- (a) One outcome is a 5, so the probability is 16.
- (b) Two outcomes (1 and 2) are less than 3, so the probability is 26 = 13.
- (c) No face shows 7, so it is impossible: the probability is 0.
Answer: (a) 16 (b) 13 (c) 0
Fractions, decimals and percentages
A bag holds 3 red, 2 blue and 5 green counters. One counter is chosen without looking. Write the probability of each colour as a fraction, a decimal and a percentage.
- There are 3 + 2 + 5 = 10 counters.
- Red: 310 = 0.3 = 30%.
- Blue: 210 = 0.2 = 20%.
- Green: 510 = 0.5 = 50%.
- Check: 30% + 20% + 50% = 100%.
Answer: Red 0.3 (30%), blue 0.2 (20%), green 0.5 (50%).
Expected and observed results
A spinner has 4 equal sections, one of them yellow. It is spun 80 times and lands on yellow 23 times. Compare the observed and expected results.
- The probability of yellow is 14 = 0.25 = 25%.
- Expected number of yellows: 14 × 80 = 20.
- Observed: 23 out of 80. That is 3 more than expected.
- A difference of 3 in 80 spins is quite normal for a chance experiment.
Answer: We expected about 20 yellows and observed 23, which is close to what we expected.
Practice check
Have a go, then check your answers. Each answer comes with an explanation.
Answer guide for parents
What is the probability of an impossible event?
0 — Impossible events have a probability of 0, the lowest point on the probability scale.
What is the probability of rolling a 5 on a standard six-sided die?
1/6 — There are 6 equally likely outcomes and only one of them is a 5, so the probability is 16.
A bag holds 4 red and 6 blue counters. What is the probability of choosing red, written as a decimal?
0.4 — There are 10 counters and 4 are red, so the probability is 410 = 0.4.
Which of these probabilities shows the most likely event?
1/2 — Write them all as decimals: 0.2, 0.35, 0.5 and 0.45. The largest is 0.5, which is 12.
A fair coin is flipped. What is the probability of heads, written as a percentage?
50% — Heads is one of two equally likely outcomes: 12 = 0.5 = 50%.
A spinner has 8 equal sections and 2 of them are green. What is the probability of landing on green, as a fraction in simplest form? (Type your answer like 1/2.)
1/4 — 2 of the 8 equal sections are green: 28 = 14.
A standard die is rolled 120 times. About how many times would you expect to roll a 3?
20 — The probability of a 3 is 16, and 16 × 120 = 120 ÷ 6 = 20.
A coin is flipped 50 times and lands heads 28 times. What percentage of the flips were heads?
56% — 2850 = 56100 = 56%. This is a little more than the expected 50%, which is normal.
Watch out for
- Writing probabilities greater than 1 or as whole numbers, such as “a 1 in 6 chance is 6”. Remind the learner that every probability sits between 0 and 1 (or 0% and 100%).
- Expecting observed results to match expected results exactly. Run experiments several times to see how results vary.
- Thinking past results change future chances, such as “heads is due after five tails”. Each flip of a fair coin still has a probability of 12.
Tips for parents
- Draw a probability line from 0 to 1 and place everyday events on it, such as “the sun will rise tomorrow” (1) or “it will snow indoors” (0).
- Let the learner do real experiments with dice, coins and counters, and record the results in a tally table.
- Practise switching between fractions, decimals and percentages using the probabilities from each experiment.
Go further
- Roll a die 60 times, record the results and compare the observed frequency of each number with the expected 10. Combine results with others to reach 300 rolls and compare again.
- Design a spinner so that the probability of red is 0.5, blue is 0.25 and green and yellow are 0.125 each. How many equal sections do you need?
- Find the probability of each total when two dice are rolled by listing all 36 outcomes in a table. Which total is most likely?
About 45 minutes
You'll need
- A coin and a standard six-sided die
- A bag with coloured counters or blocks (for example 3 red, 2 blue and 5 green)
- Paper and pencil for tally tables
- A calculator (optional)
Key words
- Probability
- A number from 0 to 1 that describes how likely an event is to happen.
- Event
- One outcome, or a group of outcomes, in a chance experiment, such as rolling an even number.
- Impossible
- Cannot happen. An impossible event has a probability of 0.
- Certain
- Will definitely happen. A certain event has a probability of 1.
- Expected frequency
- The number of times we expect an outcome over many trials, found by multiplying the probability by the number of trials.
- Observed frequency
- The number of times an outcome actually happened in an experiment.
Still tricky?
For parents
Want an outside view of where your child is at?
Book a free, no-obligation English and maths assessment at a Success Tutoring centre and get a clear starting point.
Book a free assessmentRelated probability lessons
Build up to it (Year 6)
Next steps (Year 8)