What students learn in AC9M8P01
This unit helps students build a clear, usable understanding of That complementary events have a combined probability of one; use.... The goal is not to memorise one answer pattern. Students should be able to explain the idea, recognise it in a new example and apply it in a short practice or worksheet task.
- Start with the main idea: recognise that complementary events have a combined probability of one; use this relationship to calculate probabilities in applied contexts.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- understanding that knowing the probability of an event allows the probability of its complement to be found, including for those events that are not equally likely, such as getting a specific novelty toy in a supermarket promotion using the relationship that for a single event A, Pr(A)+Pr(\;not\;A)\;=\;1; for example, if the probability that it rains on a particular day is 80\%, the probability that it does not rain on that day is 20\%, or the probability of not getting a 6 on a single roll of a fair dice is 1-\frac16=\frac56
- Finish with mixed questions so students must choose the correct strategy rather than copy the last example.
Curriculum coverage and elaborations
The content description and elaborations below show the curriculum ideas taught in this unit. Items marked as teaching context support lesson planning but may not appear in the initial eight-question activity.
- Content description: recognise that complementary events have a combined probability of one; use this relationship to calculate probabilities in applied contexts
- E1: understanding that knowing the probability of an event allows the probability of its complement to be found, including for those events that are not equally likely, such as getting a specific novelty toy in a supermarket promotion
- E2: using the relationship that for a single event A, Pr(A)+Pr(\;not\;A)\;=\;1; for example, if the probability that it rains on a particular day is 80\%, the probability that it does not rain on that day is 20\%, or the probability of not getting a 6 on a single roll of a fair dice is 1-\frac16=\frac56
- E3: using the sum of probabilities to solve problems, such as the probability of starting a game by throwing a 5 or 6 on a dice is \frac13 and probability of not throwing a 5 or 6 is \frac23
- E4: investigating how various applications of artificial intelligence use the probability of complementary events when assessing the likelihood of favourable and unfavourable outcomes and making informed decisions based on these probabilities; for example, in binary classification problems where data is classified into one of two categories, such as spam or not spam, fraud or not fraud
How to use this unit
Read the topic guide, use the teacher slide for instruction, then complete the Worksheet, Practice and Test. These three activities use the same eight-question unit bank.
Teacher resource
AC9M8P01 teacher slide
Use this one-page PDF to introduce the key idea, vocabulary and teaching sequence before students begin the activities.
Open teacher slide (PDF)Common mistakes to watch for
- Rushing to a rule before checking the concrete model, drawing or number sentence.
- Using the correct answer once but not being able to explain why it works.
- Mixing up similar vocabulary such as more/less, before/after, longer/shorter or equal groups/sharing.
International curriculum mapping
This table gives closest-topic mapping for search and planning. The Australian Curriculum code is exact; overseas entries are broad equivalents because each jurisdiction structures outcomes differently.
| Region | Curriculum | Closest mapping |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M8P01 — recognise that complementary events have a combined probability of one; use this relationship to calculate probabilities in applied contexts |
| Victoria | Victorian Curriculum F-10 | Year 8 Maths: closest match in Probability. Use this page as a VIC-aligned practice and worksheet reference. |
| NSW | NSW Curriculum | Stage 4 Maths: closest content focus for That complementary events have a combined probability of one; use... and related outcomes. |
| United States | Common Core / NGSS | Grade 8 Common Core Mathematics/ELA closest topic match for That complementary events have a combined probability of one; use.... |
| England / UK | National Curriculum | Key Stage 3 / Year 8: closest programme-of-study match for That complementary events have a combined probability of one; use.... |
| Canada | Provincial and territory curricula | Grade 8 closest topic match. Canada varies by province, so use this as a broad Ontario/BC-style learning outcome reference. |
| New Zealand | New Zealand Curriculum | Level 4 Maths: closest achievement-objective topic for That complementary events have a combined probability of one; use.... |
| India | NCERT / CBSE | Class 8 closest NCERT/CBSE topic match for That complementary events have a combined probability of one; use.... |