Primary 5 · Mathematics · Probability
Chance experiments
List the possible outcomes of chance experiments, carry out repeated trials and compare the results with what was expected.
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These lessons were written around Australian Curriculum strands and matched to Singapore levels by age (Primary 1 is the first year of primary school). They are not aligned to MOE syllabuses or the PSLE, so check them against the syllabus your child is working towards.
Learning goals
Learners will
- List all the possible outcomes of a chance experiment.
- Recognise whether outcomes are equally likely or not equally likely.
- Carry out repeated trials and compare the results with what was expected.
Success looks like
- I can list every possible outcome when I flip a coin, roll a die or spin a spinner.
- I can explain why some outcomes are more likely than others.
- I can record the results of many trials in a table and compare them with my prediction.
The big idea
In a chance experiment, we know what could happen but not what will happen. Each possible result is called an outcome.
- Flipping a coin has 2 outcomes: heads or tails.
- Rolling a standard die has 6 outcomes: 1, 2, 3, 4, 5 or 6.
- A spinner with 4 equal sections coloured red, blue, green and yellow has 4 outcomes.
When every outcome has the same chance, they are equally likely. A fair coin is equally likely to land heads or tails. But some experiments are not equally likely. On a spinner where half is red, a quarter is blue and a quarter is yellow, red is more likely than blue or yellow because it takes up more of the spinner.
We can use the chances to predict results over many trials. If a coin is flipped 20 times, we expect about half to be heads, so about 10. If a die is rolled 60 times, each number has 1 chance in 6, so we expect each number about 60 ÷ 6 = 10 times.
Real results rarely match the prediction exactly. You might flip 20 coins and get 12 heads, and that is perfectly normal. Chance means results vary, especially with only a few trials. The more trials you do, the closer the results tend to get to what you expected.
To run an experiment, make a prediction, record each trial with tally marks, count the results and then compare them with the prediction. Talk about whether the results were close and why they might differ.
Worked examples
Listing outcomes
A bag holds 3 red, 2 blue and 1 green counter. One counter is taken out without looking. List the possible outcomes. Are they equally likely?
- The counter could be red, blue or green, so there are 3 possible outcomes (colours).
- There are more red counters (3) than blue (2) or green (1).
- So the outcomes are not equally likely: red is most likely and green is least likely.
Answer: The outcomes are red, blue and green. They are not equally likely; red is most likely.
Predicting results
A spinner has 4 equal sections: red, blue, green and yellow. It is spun 40 times. About how many times would you expect it to land on blue?
- There are 4 equally likely outcomes, so blue should come up about 1 time in every 4 spins.
- 40 ÷ 4 = 10.
Answer: About 10 times.
Comparing results with predictions
A coin was flipped 30 times and landed heads 18 times. The prediction was about 15. Is the coin unfair?
- The expected number of heads is half of 30, which is 15.
- 18 is 3 more than 15. Small differences like this happen often with only 30 flips.
- To be more confident, flip it many more times, such as 200 times, and see if heads stays well above half.
Answer: We cannot tell from 30 flips. A difference of 3 is normal; more trials would give a better picture.
Practice check
Have a go, then check your answers. Each answer comes with an explanation.
Answer guide for parents
What are the possible outcomes when you roll a standard six-sided die?
1, 2, 3, 4, 5, 6 — A standard die has six faces numbered 1 to 6, so there are six possible outcomes.
A fair coin is flipped 50 times. About how many heads would you expect?
25 — Heads and tails are equally likely, so we expect about half: 50 ÷ 2 = 25.
A spinner is half red, one quarter blue and one quarter yellow. Which colour is it most likely to land on?
Red — Red takes up half the spinner, more than blue or yellow, so it is the most likely outcome.
A bag has 3 red marbles and 1 blue marble. One marble is picked without looking. Which statement is true?
Red is more likely than blue. — There are 3 red marbles and only 1 blue, so red is more likely. It is not certain, because blue could still be picked.
How many possible outcomes are there when you flip a coin?
2 — A coin can land heads or tails, so there are 2 outcomes.
A spinner has 5 equal sections numbered 1 to 5. It is spun 100 times. About how many times would you expect it to land on 3?
20 — Each of the 5 numbers is equally likely, so we expect each about 100 ÷ 5 = 20 times.
A die is rolled 60 times. About how many times would you expect to roll a 6?
10 — Each of the 6 numbers is equally likely, so we expect each about 60 ÷ 6 = 10 times.
Lily rolled a die 12 times and got a six only once, but she expected about 2 sixes. What is the best explanation?
Results from a small number of trials often differ from what we expect. — Chance results vary, especially over only 12 trials. Getting 1 six instead of 2 is very common.
Watch out for
- Expecting results to match predictions exactly, such as exactly 10 heads in 20 flips. Run the experiment several times to show how results vary.
- Believing a result is “due”, for example that tails must come next after several heads. Each flip is a fresh start; the coin does not remember.
- Thinking all outcomes are equally likely just because they are possible. Compare a spinner with equal sections to one with unequal sections.
Tips for parents
- Do the experiments for real. Rolling, flipping and spinning are much more convincing than reading about them.
- Ask the learner to predict before every experiment, then talk about how close the results were.
- Combine results from several family members to show that more trials usually give results closer to the prediction.
Go further
- Make a spinner with unequal sections (for example, half red, a quarter blue and a quarter green), spin it 40 times and compare the results with your predictions.
- Roll two dice 50 times and record the totals. Which totals come up most often? Can you explain why?
- Flip a coin 10 times, then 50 times, then 100 times. Work out what fraction of the flips were heads each time. What do you notice?
About 45 minutes
You'll need
- A coin
- A standard six-sided die
- Paper, a pencil and a paperclip to make a spinner
- A bag with coloured counters, blocks or buttons
Key words
- Chance experiment
- An activity where the result depends on chance, such as rolling a die.
- Outcome
- One possible result of a chance experiment. Rolling a die has 6 possible outcomes.
- Trial
- One go at a chance experiment, such as one flip of a coin.
- Equally likely
- Having the same chance of happening, like heads and tails on a fair coin.
- Expected result
- What we predict will happen over many trials, based on the chances of each outcome.
Still tricky?
For parents
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