Expected versus observed outcomes | Year 6

01 / LEARN

Understand the idea.

Expected means predicted, not promised

An expected count is a prediction from a chance model. Keep the probability the same for every trial, then multiply it by the number of trials. A green chance of $\frac{1}{4}$ over forty spins predicts one quarter of forty.

Expected does not mean guaranteed. Even with a fair spinner, a particular set of forty spins can contain more or fewer than ten greens. A difference is possible through random variation and does not by itself prove that the model is wrong.

expected count = number of trials \times P (event)

Observed frequencies come from records

An observed frequency is the count actually recorded. Add all outcome counts to check that they match the trial total. To express an observed relative frequency, divide the count for the chosen outcome by that total.

The supplied records show fourteen greens in forty spins, compared with ten expected. Keep both numbers distinct: one comes from the model and the other from the experiment. Report the difference honestly rather than changing results to match a prediction.

Supplied practice results: 40 spins of a fair four-colour spinner
Colour	Observed frequency
Red	8
Blue	9
Green	14
Yellow	9

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Predict a green count

A fair spinner has four equally likely colours. Predict the number of greens in 40 spins.

Worked solution

1
Identify the probability of green.
$P (green) = \frac{1}{4}$
One of the four equally likely colours is green.
2
Calculate one quarter of forty spins.
$40 \times \frac{1}{4} = 40 \div 4 = 10$
Expected count equals the trial count multiplied by the probability on each trial.
3
Interpret the prediction.
Ten greens are expected, but random variation means forty actual spins need not produce exactly ten.

Answer

10 greens expected; not guaranteed.

EXAMPLE 02

Compare prediction and data

Using the supplied practice results, compare the predicted and observed green counts.

Supplied practice results: 40 spins of a fair four-colour spinner
Colour	Observed frequency
Red	8
Blue	9
Green	14
Yellow	9

Worked solution

1
Check the total observed count.
$8 + 9 + 14 + 9 = 40$
All four colour counts together account for the forty recorded spins.
2
Calculate the expected green count.
$40 \times \frac{1}{4} = 10$
Green is one of four equally likely colours in the fair-spinner model.
3
Read the observed green count.
$observed greens = 14$
The green row of the supplied table records fourteen actual results.
4
Find the difference from the prediction.
$14 - 10 = 4$
The observed count is four above the expected count; this is a comparison, not proof of unfairness.

Answer

Observed 14; expected 10; difference 4.

03 / YOUR TURN

Try it yourself.

Check your understanding

A fair die is rolled 60 times. How many sixes are expected?

Show answer & reasoning

10.

A fair die has one six among six equally likely faces, giving probability $\frac{1}{6}$ each roll. The expected count in sixty rolls is $60 \times \frac{1}{6} = 10$ sixes.

Keep practising

6 worksheet questions · 12 marks

Open worksheet Worked solutions

Read the questions online

How many heads are expected in 20 tosses of a fair coin?
2 marks
An event has probability $\frac{1}{5}$ . How many successes are expected in 50 trials?
2 marks
A fair coin gives 27 heads in 50 tosses. Find the observed percentage of heads.
2 marks
Using the supplied spinner results, how many fewer reds occurred than expected?
2 marks
Supplied practice results: 40 spins of a fair four-colour spinner
Colour Observed frequency
Red 8
Blue 9
Green 14
Yellow 9
A student changes the observed green frequency from 14 to 10 because the spinner should be fair. Explain the problem.
2 marks
A bag model gives a blue probability of 0.3. Predict blue counts in 100 trials, then explain whether 34 blue results proves the model wrong.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

How many heads are expected in 20 tosses of a fair coin?
2 marks
$20 \times \frac{1}{2} = 10$ .
10.
An event has probability $\frac{1}{5}$ . How many successes are expected in 50 trials?
2 marks
$50 \div 5 = 10$ .
10.
A fair coin gives 27 heads in 50 tosses. Find the observed percentage of heads.
2 marks
$\frac{27}{50} = \frac{54}{100} = 54 %$ .
$54 %$ .
Using the supplied spinner results, how many fewer reds occurred than expected?
2 marks
Supplied practice results: 40 spins of a fair four-colour spinner
Colour Observed frequency
Red 8
Blue 9
Green 14
Yellow 9
Expected reds: $40 \div 4 = 10$ .
Observed reds: 8; $10 - 8 = 2$ .
2 fewer.
A student changes the observed green frequency from 14 to 10 because the spinner should be fair. Explain the problem.
2 marks
Recorded results must be retained unless a recording error is established.
Fairness does not guarantee an exact expected count.
The student has replaced evidence with a prediction.
A bag model gives a blue probability of 0.3. Predict blue counts in 100 trials, then explain whether 34 blue results proves the model wrong.
2 marks
$100 \times 0.3 = 30$ .
A difference of four can occur through random variation; further evidence would be needed.
30 expected; 34 alone does not prove the model wrong.

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Curriculum reference & lesson scope

Australian Curriculum v9.0; SA Mathematics Curriculum 2026

Numerical likelihood; fractions/decimals/percentages; expected versus observed outcomes; larger simulations and variation.

Official curriculum source ↗

In this lesson

Understand the idea.

Expected means predicted, not promised

Observed frequencies come from records

See the method in action.

Predict a green count

Identify the probability of green.

Calculate one quarter of forty spins.

Interpret the prediction.

Compare prediction and data

Check the total observed count.

Calculate the expected green count.

Read the observed green count.

Find the difference from the prediction.

Try it yourself.

Check your understanding

Keep practising