Year 5 · Mathematics · Probability
Chance and likelihood
Describe how likely everyday events are using words such as impossible, unlikely, even chance, likely and certain, and test predictions with simple 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.
These lessons were written around Australian Curriculum strands and matched to New Zealand year levels by age (NZ Year 1 is the first year of school). They are not yet mapped to The New Zealand Curriculum, so check them against your own learning programme.
Learning goals
Learners will
- Describe the chance of everyday events using the language of chance.
- Order events from least likely to most likely.
- Carry out a simple chance experiment and compare results with predictions.
Success looks like
- I can describe an event as impossible, unlikely, even chance, likely or certain.
- I can explain why one outcome is more likely than another.
- I can record the results of a chance experiment in a tally table.
The big idea
Some things are sure to happen and some things can never happen. Most things are somewhere in between. We use special words to describe chance, and we can place them along a line from impossible to certain:
- Impossible – rolling a 7 on a standard six-sided die.
- Unlikely – picking a blue counter from a bag with 1 blue and 9 red counters.
- Even chance – flipping a coin and getting heads.
- Likely – picking a red counter from that same bag with 9 red and 1 blue counters.
- Certain – rolling a number less than 7 on a standard six-sided die.
To decide how likely something is, think about all the possible outcomes and how many of them give the result you want. A standard die has 6 outcomes: 1, 2, 3, 4, 5 and 6. Only one of them is a 6, so rolling a 6 is unlikely. Three of them are even (2, 4 and 6), so rolling an even number has an even chance.
Chance experiments do not always turn out exactly as predicted. If you flip a coin 10 times you might get 6 heads and 4 tails. That is normal. The more times you repeat an experiment, the closer the results usually get to what you expect.
Worked examples
Describing a spinner
A spinner has 4 equal sections coloured red, red, red and green. Describe the chance of landing on green.
- Count the outcomes: there are 4 equal sections.
- Only 1 of the 4 sections is green.
- Landing on green could happen, but it will probably not happen.
Answer: Landing on green is unlikely.
Ordering events
Order these from least likely to most likely when rolling a standard six-sided die: rolling a 0; rolling a 5; rolling a number greater than 1.
- Rolling a 0 is impossible because 0 is not on the die.
- Rolling a 5 is 1 out of 6 outcomes, so it is unlikely.
- Rolling a number greater than 1 means rolling 2, 3, 4, 5 or 6, which is 5 out of 6 outcomes, so it is likely.
Answer: Rolling a 0, then rolling a 5, then rolling a number greater than 1.
Testing a prediction
Put 3 yellow and 3 blue counters in a bag. Predict, then test, how often you will pick yellow in 20 picks (putting the counter back each time).
- There are 6 counters and 3 are yellow, so yellow has an even chance.
- An even chance suggests about half of the 20 picks, which is about 10, will be yellow.
- Do the experiment and record a tally. A result such as 9 or 12 yellows is close to the prediction and is perfectly normal.
Answer: We predict about 10 yellows, and results near 10 match the even chance.
Practice check
Have a go, then check your answers. Each answer comes with an explanation.
Answer guide for parents
How would you describe the chance of rolling a 7 on a standard six-sided die?
Impossible — A standard die only has the numbers 1 to 6, so rolling a 7 is impossible.
How would you describe the chance of flipping a coin and getting heads?
Even chance — A coin has two sides, heads and tails, which are equally likely. So heads has an even chance.
A bag holds 9 red marbles and 1 blue marble. How would you describe the chance of picking a red marble without looking?
Likely — 9 of the 10 marbles are red, so picking red will probably happen. It is likely, but not certain.
Which of these events is certain?
Rolling a number less than 7 on a six-sided die — Every number on a standard die (1 to 6) is less than 7, so this will always happen.
A spinner has 4 equal sections coloured red, red, red and green. Which colour is the spinner most likely to land on?
Red — 3 of the 4 equal sections are red, so red is the most likely colour.
A bag has 3 yellow counters and 3 blue counters. Using chance words, how likely is it that you pick a yellow counter?
Even chance — Half of the counters are yellow, so picking yellow is just as likely as not picking yellow.
How many different outcomes are possible when you roll a standard six-sided die once?
6 — The die could land on 1, 2, 3, 4, 5 or 6, which is 6 outcomes.
A bag has 5 green, 2 orange and 1 purple counter. Which colour are you least likely to pick?
Purple — There is only 1 purple counter, which is fewer than any other colour.
Watch out for
- Believing that some numbers on a die are “harder” to roll, such as 6. On a fair die each number has the same chance.
- Thinking that after several heads in a row, tails is “due”. A coin has no memory; each flip still has an even chance.
- Using “likely” to mean “certain”. Stress that likely events can still fail to happen.
Tips for parents
- Use chance words in everyday talk: “Is it likely to rain today?” or “Is it certain we'll have pasta tonight?”
- When an experiment does not match the prediction, treat it as interesting rather than wrong, and talk about why results vary.
- Ask the learner to justify their answers by counting the possible outcomes.
Go further
- Make your own spinner from cardboard and a paperclip, colour it so that blue is likely and red is unlikely, then test it 30 times.
- Roll a die 60 times and tally the results. Compare the totals for each number and discuss what you notice.
- Create a chance line across a page from impossible to certain and place at least eight events from your own life along it.