Year level: 9

Strand: Probability

Lesson length: 60 mins

Smashing good fun learning about probability without replacement, by playing and exploring the game of egg roulette – 12 eggs, 3 raw and 9 cooked. Contestants take it in turns to choose an egg and smash it on their head hoping to avoid the 3 raw eggs!

In a Part 2, students consolidate and make deeper connections using simulation to address misconceptions on this abstract concept.

Achievement standard

By the end of Year 9, students determine sets of outcomes for compound events and represent these in various ways, assign probabilities to the outcomes of compound events and design and conduct experiments or simulations for combined events using digital tools.

Content description

• Students list all outcomes for compound events both with and without replacement, using lists, tree diagrams, tables or arrays; assign probabilities to outcomes. AC9M9P01
• Students calculate relative frequencies from given or collected data to estimate probabilities of events involving ‘and’, inclusive ‘or’ and exclusive ‘or’. AC9M9P02
• Students design and conduct repeated chance experiments and simulations, using digital tools to compare probabilities of simple events to related compound events, and describe results. AC9M9P03

General capabilities

Numeracy progression

• Probabilistic reasoning (Level 6)

Digital literacy

Critical and creative thinking:

• Draw conclusions and provide reasons (Level 6)

The following suggestions is suggested as part of on-going assessment for Part 1 of this lesson sequence.

Collect students’ Egg-cellent worksheets to review before next lesson to individually assess how students are progressing and whether they are understanding the main concepts so far. Remember to redistribute the worksheets for students to complete at the beginning of the next lesson.

Consider further scaffolding activities for particular students to practise either for homework or in class during Egg roulette: Part 2.

• Students may believe that the probability of an event occurring in a two or three-stage probability experiment is the same as the probability of the event occurring in a one-stage experiment. The impact of an experiment without replacement is Illustrated via egg roulette, where it is clear that eggs are ‘used up’ and no longer appear in the sample space in later stages. This misconception is addressed through detailed modelling of the sample space using a table approach for the first two stages.
• Students may assume that outcomes are equally likely. The distribution of cooked / raw eggs has been deliberately chosen to be heavily skewed towards cooked eggs. Students can be asked questions such as, ‘Are there more cooked or raw eggs?’ ‘Is it more likely [person] gets a cooked or raw egg? Explain why.’
• Students may be confused with the discrepancies between theoretical and experimental probabilities. An example such as tossing a coin once could be used where it is impossible to get half a head. Using the simulation to increase to a large number of trials allows for illustration of the Law of Large Numbers, reducing the discrepancy between the two.

Key language: compound event with and without replacement, simulation, two-stage compound event, relative frequency, ‘and’ and ‘or’ statements, ‘inclusive or’ and ‘exclusive or’ statements.