- explain the central idea: Use conditional-probability language precisely and identify how the relevant sample space changes when information is given.
- choose and apply an appropriate method without relying on keyword matching
- check results using units, substitution, estimation, a second representation or contextual reasonableness
- justify a conclusion and communicate limitations where the context requires them
Year 10 Mathematics · AC9M10P01
Conditional Probability Language
Words such as “given” or “knowing that” restrict the sample space. The denominator must match the condition before a conditional probability can be interpreted correctly
Ready to project and teach
Learning goalsSay it simply
Key conceptTeach from the board
P(A|B) means “probability of A given B”. Once B is known, only outcomes inside B remain possible. Independent events satisfy P(A|B)=P(A); dependent events do not.
Notation
P(A|B)=P(A∩B)/P(B), if P(B)>0.
Language
“of B”, “given B”, “knowing B” → denominator is B group/sample space.
Independent
P(A|B)=P(A).
Tree
Multiply along branches; branch probabilities may change after a dependent outcome.
Worked examplesWe do
Worked examples
AC9M10P01 - Conditional Probability Language
Example 1
Notation P(A|B)=P(A∩B)/P(B), if P(B)>0.
Example 2
Language “of B”, “given B”, “knowing B” → denominator is B group/sample space.
Example 3
Tree Multiply along branches; branch probabilities may change after a dependent outcome.
Example 4
: use two-way tables/Venn diagrams to interpret conditional statements and common language errors. Examples 1–3,8.
Curriculum examplesCopied content
Australian Curriculum: AC9M10P01 — Year 10 Probability. Use conditional-probability language precisely and identify how the relevant sample space changes when information is given.
Victoria: VC2M10P01 — Level 10 Probability
NSW: Stage 5 Core — Probability; Path — Further probability
Alignment explanation: The explicit teaching and worked examples address the Australian Curriculum concept directly. The Victorian mapping follows the current Version 2.0 descriptor structure; where Victoria combines or extends content, that difference is stated rather than hidden. NSW uses a Stage 5 Core–Paths structure, so this page maps to the relevant content group(s) and Working mathematically processes instead of inventing a Year 10 one-to-one code.
| Lesson component | Australian Curriculum | Victoria | NSW |
|---|---|---|---|
| Explicit concept teaching and worked examples | AC9M10P01 | VC2M10P01 — Level 10 Probability | Stage 5 Core — Probability; Path — Further probability |
| Guided and independent practice | Builds fluency and application for AC9M10P01 | Practises the mapped Level 10/10A knowledge as applicable | Practises the mapped Stage 5 Core/Path content |
| Reasoning and assessment tasks | Applies reasoning/problem solving in the descriptor context | Supports Victorian reasoning and modelling expectations | Embeds Working mathematically: reasoning, problem solving and communication |
Australian Curriculum elaborations
AC9M10P01: use language of “if ... then”, “given”, “of”, “knowing that” to describe and interpret conditional probability.
- E1: use two-way tables/Venn diagrams to interpret conditional statements and common language errors. Examples 1–3,8.
- E2: use arrays/tree diagrams to represent and compare dependent/independent events. Examples 4–7.
- E3: investigate conditional probability in NLP tasks such as generation, translation, augmentation and recommendations. Examples 9–10.
Questions and answersWith answers
- 30 of 50 juniors choose X. Find P(X|junior).
- 0.6.
- 20 of 40 X-choosers are seniors. Find P(senior|X).
- 0.5.
- If |B|=25 and |A∩B|=5, find P(A|B).
- 0.2.
Practice and reviewReady for practice
- Swapping P(A|B) and P(B|A).
- Using total sample as denominator after a condition is given.
- Assuming events are independent without checking.
- Keeping branch probabilities unchanged in sampling without replacement.
- Reading “if…then” as ordinary implication without identifying the restricted probability group.
Curriculum alignmentStart here
- explain the central idea: Use conditional-probability language precisely and identify how the relevant sample space changes when information is given.
- choose and apply an appropriate method without relying on keyword matching
- check results using units, substitution, estimation, a second representation or contextual reasonableness
- justify a conclusion and communicate limitations where the context requires them
- Australian Curriculum Version 9 — ACARA
- Victorian Curriculum Mathematics Version 2.0 — VCAA
- NSW Mathematics K–10 Syllabus (2022) — NSW Curriculum/NESA
Official wording is paraphrased on SkillrHub; use the linked curriculum sites as the source of record.
Other curriculum comparisons retained
US closest CCSS HSS-CP.A.3–5; UK GCSE conditional probability/tree diagrams; NSW Stage 5 and Victorian Level 10 probability; comparable Canadian/NZ secondary conditional probability.
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