The idea, step by step
What “not” includes
The complement of an event contains every possible outcome outside it. The event and its complement cannot happen together, and together they cover the whole sample space. On a die, “not 6” includes 1,2,3,4,5, not just one other number.
Probabilities total one
Therefore . The same rule works with fractions, decimals and percentages. If an event is impossible, its complement is certain; if certain, its complement is impossible. Check that a probability lies from 0 to 1, or from 0% to 100%.
A common trap
The complement of red always means blue.
Instead: It includes every non-red outcome, including any other colours.
See the thinking
Worked example 1
Find P(not 6) for a fair die.
- P(6)=1/6.
- 1−1/6=5/6.
Worked example 2
A spinner has 10 equal sectors: 3 blue,4 red,3 yellow. Find P(not blue).
- There are 7 non-blue sectors.
- 7/10=1−3/10.
Check your understanding
If P(win)=0.28, find P(not win).
Show answer
0.72.
1−0.28=0.72.
Your turn
6 questions · 12 marks · Work at your own pace.
Read the questions online
- Find P(not 1) for a fair standard die.2 marks
- If P(rain)=0.35, find P(no rain).2 marks
- A bag has 4 red,3 blue,5 green tokens. Find P(not green) for a random draw.2 marks
- An event has probability 72%. Find the complement probability.2 marks
- Why are even and odd outcomes complements on a standard die?3 marks
- Find the complement probability of an impossible event.1 mark
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Find P(not 1) for a fair standard die.2 marks
Five of six equally likely outcomes are not 1.
5/6. - If P(rain)=0.35, find P(no rain).2 marks
1−0.35=0.65.
0.65. - A bag has 4 red,3 blue,5 green tokens. Find P(not green) for a random draw.2 marks
There are 12 tokens and 7 are not green.
7/12. - An event has probability 72%. Find the complement probability.2 marks
100%−72%=28%.
28%. - Why are even and odd outcomes complements on a standard die?3 marks
Every die outcome belongs to exactly one of the two sets.
They do not overlap and together cover all six outcomes. - Find the complement probability of an impossible event.1 mark
1−0=1.
1.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum
Complementary events; two-stage sample spaces; tables, trees and Venn diagrams; probabilities of combined outcomes; experimental versus theoretical results; compound-event simulations and describing results. Formal conditional probability is Year 10.
Official curriculum source ↗