AC9M4P01: Describe possible everyday events and the possible outcomes of chance experiments and order outcomes or events based on their likelihood of occurring; identify independent or dependent events

Likelihood depends on the possible outcomes and conditions. Events are independent when one result does not change the chance of the next; they are dependent when the first event changes the available outcomes or conditions.

Learning routine: Define experiment → List complete outcomes → Compare favourable outcomes → Order likelihood → Check replacement/conditions → Classify dependence

Success looks like

• List complete outcomes
• Order likelihood
• Use evidence/conditions
• Identify independence
• Identify dependence

outcome

a possible result of a chance event

likelihood

how likely an outcome is

dependent event

an event whose chance is affected by an earlier result

The content description and elaborations below show the curriculum ideas taught in this unit. Items marked as teaching context support lesson planning.

• Content description: describe possible everyday events and the possible outcomes of chance experiments and order outcomes or events based on their likelihood of occurring; identify independent or dependent events
• E1: using lists of events familiar to students and ordering them from “least likely” to “most likely” to occur; considering and discussing why the order of some events might be different for different students
• E2: predicting the outcome of a coin toss after 5 heads have been flipped in a row, discussing the assertion that because so many heads came up, it is more likely that a tail rather than a head will come up next; discussing with reasons why the assumption is correct or incorrect
• E3: predicting how likely, from least likely to most likely, of selecting a red ball from a bag containing 10 red balls and 5 white balls, a bag containing 20 of each, or one that has 25 red balls and 20 white balls, justifying their decision
• E4: identifying school activities where the chance of them taking place is affected by the chance of other events occurring; for example, given that there is a high chance of a storm on Friday, there is only a small chance that the coastal dune planting project will go ahead
• E5: listing the outcomes of everyday chance situations and identifying where one cannot happen if the other happens; for example, discussing that it cannot be hot and cold at the same time; selecting a card from a deck and discussing if it is red it cannot be a spade or a club
• E6: identifying different dependent events where the chance of one outcome occurring will be affected by the occurrence of other outcomes and different independent events where the chance of one outcome occurring will not be affected by the occurrence of other outcome(s)
• E7: exploring how ordering outcomes based on their likelihood of occurring is an essential component of early warning systems that use artificial intelligence to make decisions, such as natural disaster warning systems
• E8: discussing how likelihood relates to the decisions an artificial intelligence tool makes when generating predictive text; for example, discussing which word would most likely come next in a sentence, then refining the decision as the first letter is revealed

Core idea: Likelihood depends on the possible outcomes and conditions. Events are independent when one result does not change the chance of the next; they are dependent when the first event changes the available outcomes or conditions.

Remember

• List complete outcomes
• Order likelihood
• Use evidence/conditions
• Identify independence
• Identify dependence

Important questions

• Order impossible, unlikely, likely and certain events. Explain using the model or evidence above.
• List outcomes for two coin tosses. Explain using the model or evidence above.
• Explain replacement. Explain using the model or evidence above.
• Classify two draws without replacement. Explain using the model or evidence above.
• Give independent everyday events. Explain using the model or evidence above.

Read the topic guide and use the teacher slide for instruction. Students can then use the worksheet for written work, open Practice for supported feedback, or take the Test when they are ready.

• Likely confused with certain — A likely event can still fail to occur.
• Outcome list incomplete — Use a systematic table or tree to include all ordered outcomes.
• Independent means different — Independence concerns whether one event changes the chance of another.
• Replacement condition ignored — State whether items are returned before the next draw.

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.

Official elaboration: using lists of events familiar to students and ordering them from “least likely” to “most likely” to occur; considering and discussing why the order of some events might be different for different students

List walk to school, see a bus and see snow tomorrow. Put them in a sensible order for your location; give reasons using distance, local transport and weather. Another child may reasonably order them differently. Teacher asks: Which condition changed your order? Evidence: a justified order, not a memorised universal ranking.

Official elaboration: predicting the outcome of a coin toss after 5 heads have been flipped in a row, discussing the assertion that because so many heads came up, it is more likely that a tail rather than a head will come up next; discussing with reasons why the assumption is correct or incorrect

A fair coin has shown H, H, H, H, H. Its next possible outcomes are still heads and tails, equally likely. The earlier sequence does not alter the coin. Ask learners to explain why both a sixth head and a tail remain possible. Correct the claim that chance must balance immediately.

Official elaboration: predicting how likely, from least likely to most likely, of selecting a red ball from a bag containing 10 red balls and 5 white balls, a bag containing 20 of each, or one that has 25 red balls and 20 white balls, justifying their decision

Use identical balls and a random draw. Bag A: 10 red, 5 white. B: 20 red, 20 white. C: 25 red, 20 white. Least to most chance of red is B, C, A. B has equal colours. C is only a little red-heavy. A has two red for every white; grouped models show a greater red share. More red balls alone is not enough when total contents differ. Formal probability fractions are not required.

Official elaboration: identifying school activities where the chance of them taking place is affected by the chance of other events occurring; for example, given that there is a high chance of a storm on Friday, there is only a small chance that the coastal dune planting project will go ahead

For a coastal dune planting visit, use the rule: cancel if a storm arrives. A high chance of a storm means less chance the visit goes ahead. Plan an indoor alternative. The forecast is evidence, not a guarantee; explain the stated link instead of assuming all outdoor activities follow the same rule.

Official elaboration: listing the outcomes of everyday chance situations and identifying where one cannot happen if the other happens; for example, discussing that it cannot be hot and cold at the same time; selecting a card from a deck and discussing if it is red it cannot be a spade or a club

A single card cannot be red and a spade: hearts/diamonds are red and spades/clubs are black. Red and heart can occur together. For everyday temperature comparisons, specify the same place, time and agreed hot/cold categories. Incompatibility concerns one situation; it is not the same as independence of separate trials.

Official elaboration: identifying different dependent events where the chance of one outcome occurring will be affected by the occurrence of other outcomes and different independent events where the chance of one outcome occurring will not be affected by the occurrence of other outcome(s)

Draw from 2 red and 2 blue counters. Keep red out: 1 red and 2 blue remain, so the next colour chances change. Return red and mix: 2 of each restores the original chances. Separate fair coin tosses are independent because one outcome does not alter the next toss. Do not require formal conditional-probability notation.

Official elaboration: exploring how ordering outcomes based on their likelihood of occurring is an essential component of early warning systems that use artificial intelligence to make decisions, such as natural disaster warning systems

Make a fictional early-warning card: low, medium or high chance of heavy rain using supplied observations. AI warning tools can help rank likely outcomes and update estimates as evidence changes. A high warning supports following safety advice even though the event is not certain. This classroom model is not a real forecast.

Official elaboration: discussing how likelihood relates to the decisions an artificial intelligence tool makes when generating predictive text; for example, discussing which word would most likely come next in a sentence, then refining the decision as the first letter is revealed

For Put on your ..., both coat and shoes fit. Reveal c and coat becomes the better suggestion of those two. AI predictive text uses patterns and context to rank possibilities; it can still suggest a word the writer did not intend. Ask learners to produce and explain their own two-word example.

Important questions and answers: Why is tails not owed after five heads? Earlier independent tosses do not change the next fair toss. Why can two bags with different red counts give the same chance? Both may have the same balance of colours.

Boundary: Use descriptive likelihood, conditions and observable evidence. Do not require numerical probability formulas, probability trees or formal statistical tests.

Support: Use physical objects and record one result at a time. Core: Explain each comparison using the stated conditions and actual records. Extend: Change one condition and justify what may change, within this code.

Exit evidence: Order a balanced and red-heavy bag, explain a dependent draw and correct the five-heads claim. Accept a justified red-share comparison, changed contents without replacement and unchanged next-toss chances.

Curriculum equivalents for Possible everyday events and the possible outcomes of chance experiments...

Mapped skill: describe possible everyday events and the possible outcomes of chance experiments and order outcomes or events based on their likelihood of occurring; identify independent or dependent events

These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.

Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.

• Australian Curriculum Version 9.0
• Victorian Curriculum F-10
• NSW Curriculum
• Common Core State Standards
• Next Generation Science Standards
• England National Curriculum
• New Zealand Curriculum
• NCERT textbooks

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• AC9M4N02: Explain and use the properties of odd and even numbers
• AC9M4N03: Find equivalent representations of fractions using related denominators and make connections between fractions and decimal notation
• AC9M4N04: Count by fractions including mixed numerals; locate and represent these fractions as numbers on number lines
• AC9M4N05: Solve problems involving multiplying or dividing natural numbers by multiples and powers of 10 without a calculator, using the multiplicative relationship between the place value of digits
• AC9M4N06: Develop efficient strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder
• AC9M4N07: Choose and use estimation and rounding to check and explain the reasonableness of calculations including the results of financial transactions
• AC9M4N08: Use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate the problems using number sentences and choose efficient calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation