Expected level of development
Australian Curriculum Mathematics V9: AC9M10P02
Numeracy Progression: Understanding chance: P6
At this level, students design and conduct chance experiments relating to conditional probability using digital simulation tools to conduct multiple trials. Students are expected to interpret problems and describe their interpretations.
Model different scenarios and demonstrate when conditions are dependent or independent and the effect this has on calculating probability. It is important that students can identify ‘conditionality’ so that they may choose the correct approach to analysing data and assigning probabilities. Design conditional probability scenarios with and without replacement, and repeat experiments with respect to small increases of population size. Highlight when the differences between the scenarios become negligible.
For deeper understanding, demonstrate using population data from various online data sets from the real world (for example, the Australian Bureau of Statistics), and encourage students to do the same. Using real-life scenarios or data sets illustrates how conditional probability is used, particularly in decision-making.
It is useful to show counterintuitive scenarios, such as the Monty Hall problem or the three-door problem. Use Venn diagrams and two-way tables to aid understanding in problems where the nuance in language may cause misunderstandings.
Teaching and learning summary:
- Build on students’ skill and knowledge base for conditional probability.
- Ensure students can interpret different scenarios and variations of conditional probability.
- Demonstrate how to design and experiment with digital tools so that various data sets may be analysed.
- Teach students how best to frame and describe probability analysis and results. Ensure students use correct notation.
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Teaching strategies
A collection of evidence-based teaching strategies applicable to this topic. Note we have not included an exhaustive list and acknowledge that some strategies such as differentiation apply to all topics. The selected teaching strategies are suggested as particularly relevant, however you may decide to include other strategies as well.
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Mathematics investigation
By giving students meaningful problems to solve they are engaged and can apply their learning, thereby deepening their understanding.
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Questioning
A culture of questioning should be encouraged and students should be comfortable to ask for clarification when they do not understand.
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Explicit teaching
Explicit teaching is about making the learning intentions and success criteria clear, with the teacher using examples and working though problems, setting relevant learning tasks and checking student understanding and providing feedback.
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Teaching resources
A range of resources to support you to build your student's understanding of these concepts, their skills and procedures. The resources incorporate a variety of teaching strategies.
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Conditional probability
Teachers can use this resource to prepare, plan lessons and assess students on the topic of conditional probability.
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Excel technique: conditional formatting
Use this resource to become familiar with setting up conditional probability scenarios for your students using Excel. Have students design their own scenario.
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Same number!
This NRICH resource gives teacher guidance and student solutions for a common probability problem where results may be counterintuitive due to misconceptions around conditional probability. The student-facing page is interactive and allows for varying populations sizes.
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Monty Hall problem
This GeoGebra interactive allows students to play the famous game show and challenge their intuition. Encourage students to play digitally but also to complement their thinking by creating tree diagrams and tables to help solve the problem.
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Assessment
By the end of Year 10, students can design and conduct simulations involving conditional probability, using digital tools.
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Conditional probability
Teachers can use this resource to prepare, plan lessons and assess students on the topic of conditional probability.
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The dog ate my homework
This teacher resource is a practical experiment that highlights the conditions that conditional probability imposes on scenarios. There is a link to a downloadable worksheet and to an interactive simulator.
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Matching criminals
Set this problem as a homework task, or in-class assessment or investigation. Matching DNA is interesting for students and shows them how certain scenarios are frequently used in the real world.
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