AC9M5P01: List the possible outcomes of chance experiments involving equally likely outcomes and compare to those which are not equally likely

Students define the sample space, decide whether outcomes are equally likely and express event probability as favourable equally likely outcomes over total outcomes.

For equally likely outcomes, probability = number of favourable outcomes ÷ total number of possible outcomes.

The die outcomes are equally likely if the die is fair. Count each outcome once and simplify the fraction where useful.

Do not use favourable/total counting unless elementary outcomes are equally likely or the probability structure is otherwise known.

Learning routine: Represent → Reason → Calculate → Interpret → Verify

Success looks like

• Construct or represent accurately
• Use correct vocabulary and notation
• Interpret relationships
• Apply to a new example
• Justify and evaluate

sample space

set of all possible outcomes

equally likely

having the same probability

favourable outcome

outcome included in the event

Content description: list the possible outcomes of chance experiments involving equally likely outcomes and compare to those which are not equally likely.

• E1: discussing what it means for outcomes to be equally likely and comparing the number of possible and equally likely outcomes of chance events; for example, when drawing a card from a standard deck of cards there are 4 possible outcomes if you are interested in the suit, 2 possible outcomes if you are interested in the colour or 52 outcomes if you are interested in the exact card
• E2: discussing how chance experiments that have equally likely outcomes can be referred to as random chance events; for example, if all the names of students in a class are placed in a hat and one is drawn at random, each person has an equally likely chance of being drawn
• E3: investigating how bias and fairness can relate to outcomes being equally and not equally likely, and discussing how this might inform strategies for mitigating bias in AI systems
• E4: commenting on the chance of winning games by considering the number of possible outcomes and the consequent chance of winning
• E5: investigating why some games are fair and others are not; for example, drawing a track game to resemble a running race and taking it in turns to roll 2 dice, where the first runner moves a square if the difference between the 2 dice is zero, one or 2 and the second runner moves a square if the difference is 3, 4 or 5; responding to the questions, “Is this game fair?”, “Are some differences more likely to come up than others?” and “How can you work that out?”
• E6: comparing the chance of a head or a tail when a coin is tossed, whether some numbers on a dice are more likely to be facing up when the dice is rolled, or the chance of getting a 1, 2 or 3 on a spinner with uneven regions for the numbers
• E7: discussing supermarket promotions such as collecting stickers or objects and whether there is an equal chance of getting each of them

Core idea: For equally likely outcomes, probability = number of favourable outcomes ÷ total number of possible outcomes.

Remember

• Construct or represent accurately
• Use correct vocabulary and notation
• Interpret relationships
• Apply to a new example
• Justify and evaluate

Important questions

• List a die sample space. Explain using the model or evidence above.
• Find P(even). Explain using the model or evidence above.
• Compare equal/unequal spinners. Explain using the model or evidence above.
• Write impossible/certain probabilities. Explain using the model or evidence above.
• Explain favourable outcomes. Explain using the model or evidence above.

Learn from the Topic Guide and fixed Teacher Slides, complete the Practice Sheet, use Practice for supported feedback, then take the Test when ready.

Project the fixed branded slide deck one slide at a time.

• Event names assumed equally likely — Repeated counters or unequal sectors change probability.
• Outcomes omitted or duplicated — List systematically.
• Probability fraction uses event names as denominator — Use total equally likely outcomes.
• Probability exceeds 1 — Valid probability lies from 0 to 1.

Curriculum equivalents for List the possible outcomes of chance experiments involving equally likely...

Mapped skill: list the possible outcomes of chance experiments involving equally likely outcomes and compare to those which are not equally likely

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

• AC9M5N01: Decimals Beyond Hundredths
• AC9M5N02: Factors, Multiples and Divisibility
• AC9M5N03: Comparing and Ordering Fractions
• AC9M5N04: Percentages, Fractions and Decimals
• AC9M5N05: Adding and Subtracting Fractions
• AC9M5N06: Multiplying Larger Numbers