Planning tool

Students:

• extend vocabulary and skills on probability for two-step chance experiments with and without replacement
• work in a systematic manner using tree diagrams, lists, arrays or tables to assign probabilities correctly
• attempt and assign probabilities to three-stage events
• use notation correctly.

Some students may:

• learn the rules of probability and perform well in tests, yet still demonstrate misconceptions in probability from year to year. It is important to ensure that students are given the opportunities to gain deeper understanding so that it leaves a sustained impression. It is advised to not only teach correct rules, formulas and procedures, but to demonstrate the common biases that lead to incorrect decisions for different and more complicated scenarios. Be aware of the following common biases:
  • equiprobability bias: the tendency to give equal probabilities for any chance event regardless of the actual probability. (For example, students may give equal probability to a two-event chance experiment without replacement.)
  • representativeness: the tendency to assign likelihood or judgement to an event based on what came before. (For example, results of a coin-toss experiment revealed THTHTH, so the student might think that the next event will be T.)
  • outcome orientation: treating the probability of a single outcome or non-occurrence of an event as an affirmation of certainty rather than considering the event as part of a likelihood of many events.

The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.

Learning intention

• I am learning about data sets for stepped chance problems without replacement.
• I am learning how to assign probabilities to a real-world scenario.

Why are we learning about this?

Sometimes there are fun reasons for knowing about chance and probability. How would you feel if you won first prize at a local raffle? Do you know your chances of winning? Would you buy the tickets if you knew your chances?

What to do

There is a raffle to raise money for the local footy club and a group of players is selling tickets at the game. You buy five tickets for $20 and feel good about helping out the community team. You are told the raffle for first, second and third prizes will be held after the game. You wait around so you can see if you have won any of the draws.

The time comes and the administrator of the club tells the audience that 200 tickets were sold altogether (the biggest sales yet!). Now that you know how many tickets were sold, you quickly draw a tree diagram on a napkin and think about your chances of winning one of the prizes. You wait nervously for the first prize to be drawn – a night’s accommodation at the beach!

1. What does your tree diagram look like?

2. What is the probability that you will win first prize?

You don’t win but are confident that you might win second prize – a $100 gift voucher for the local sports store.

3. What probability did you assign yourself for winning second prize?

You don’t win. One more chance!

You consult your diagram.

The third prize is about to be drawn – a meat tray! It’s not the prize you wished for but it’s always nice to win something.

4. What is the probability of winning third prize?

Success criteria

• I can confidently assign probabilities to a three-step chance problem without replacement.
• I can assign probabilities in relation to a real-world scenario.