Year 9 Mathematics · AC9M9P02

Relative Frequency and AND/OR Events

Relative frequency estimates probability from observed data. Combined events require precise language: AND means intersection, inclusive OR allows overlap, and exclusive…

Ready to project and teach

Learning goalsSay it simply

Relative frequency estimates probability from observed data. Combined events require precise language: AND means intersection, inclusive OR allows overlap, and exclusive OR excludes the overlap.

By the end of this lesson, you should be able to:

  • calculate relative frequency from data
  • use relative frequency to estimate probability
  • distinguish AND, inclusive OR and exclusive OR
  • use tables or Venn diagrams to avoid double counting
Key conceptTeach from the board

Relative frequency is an observed proportion

Relative frequency=event frequency/total trials. It can estimate an unknown probability.

AND means both conditions

A∩B is the overlap.

Inclusive OR includes overlap

P(A∪B)=P(A)+P(B)−P(A∩B), because the overlap would otherwise be counted twice.

Exclusive OR removes overlap entirely

It means A or B but not both. Read the wording carefully before choosing the event.

Worked examplesWe do

Worked examples

AC9M9P02 - Relative Frequency and AND/OR Events
Example 1

Relative frequency 37 successes in 100 trials estimates probability 0.37.

Example 2

Inclusive OR If P(A)=0.5, P(B)=0.4 and P(A∩B)=0.2, then P(A∪B)=0.7.

Example 3

Exclusive OR Using the same values, exactly one of A or B has probability 0.5+0.4−2(0.2)=0.5.

Example 4

Estimate probability from 62 successes in 200 trials.

Curriculum examplesCopied content

Australian Curriculum v9.0 — AC9M9P02: calculate relative frequencies from given or collected data to estimate probabilities of events involving “and”, inclusive “or” and exclusive “or”

Victoria: VC2M9P02 — Level 9 Probability. The mapping names direct Level 9 content where available and explicitly identifies supporting content where the Victorian structure separates an idea differently.

NSW: Stage 5 Core — Probability; Path — Further probability. NSW organises Years 7–10 Mathematics through Stage 5 Core content groups and Paths rather than a one-code-per-Year-9 structure, so this lesson does not force a false one-to-one outcome.

Lesson componentAustralian CurriculumVictoriaNSW
Concept teaching + worked examplesAC9M9P02VC2M9P02 — Level 9 ProbabilityStage 5 Core — Probability; Path — Further probability
Guided + independent practiceApplies the descriptor through progressively less-scaffolded problemsBuilds the corresponding Level 9 mathematical knowledge and fluencySupports Stage 5 Core/Path application and Working mathematically
Reasoning + assessment + masteryChecks transfer, justification, interpretation and model limitsChecks Level 9 reasoning at the mapped content depthChecks relevant Stage 5 reasoning without claiming a false Year 9 equivalent
Questions and answersWith answers
What is relative frequency?
Observed event count divided by total trials.
Why subtract overlap for inclusive OR?
It was counted once in A and once in B, so subtract one duplicate count.
What does exclusive OR mean?
One event or the other, but not both.
Practice and reviewReady for practice
  • Relative frequency is exact theoretical probability: It is an empirical estimate that varies between samples.
  • OR always means add: Subtract overlap for inclusive OR.
  • Inclusive and exclusive OR are the same: Exclusive OR removes cases where both occur.
  • AND means add probabilities: Intersection depends on joint occurrence and context.
  1. [5 marks] Use trial data to calculate relative frequencies for individual and combined events.
  2. [6 marks] Interpret a two-way table and calculate AND, inclusive OR and exclusive OR probabilities.
  3. [7 marks] Evaluate a claim that double-counts overlapping categories and correct it with clear set and probability reasoning.

Review hint: A full-mark response shows the method, keeps units and restrictions visible, interprets the result in context and checks whether the answer is reasonable.

Curriculum alignmentStart here

Relative frequency estimates probability from observed data. Combined events require precise language: AND means intersection, inclusive OR allows overlap, and exclusive OR excludes the overlap.

By the end of this lesson, you should be able to:

  • calculate relative frequency from data
  • use relative frequency to estimate probability
  • distinguish AND, inclusive OR and exclusive OR
  • use tables or Venn diagrams to avoid double counting
Related resourcesKeep teaching
Teach & ExplainTeaching slides and samples

Teach this topic step by step

Explore optional teaching slide packs for classroom lessons and explanations at home.

Browse Teach & Explain · Browse Print & Go

Teachers: follow SkillrHub on TPT, then email us to request a free sample before buying. Include the year, subject and topic or curriculum code.

Request a free sample

After trying the sample, honest feedback is welcome. A TPT review is optional, where available, and does not need to be positive.