Planning tool

Students:

• are familiar with and comfortable using the language of probability
• use online digital tools to conduct repeated chance experiments with large numbers of trials
• can predict, observe, record and distinguish between what was predicted and what has occurred during an experiment.

Some students may:

• find the concept of randomness of an event and how it may be investigated problematic. By designing and conducting experiments, students may be shown how trends can become predictable.
• confuse theoretical and experimental probability. The distinction can be shown by calculating probabilities from a sample space and then conducting the experiment. The probabilities can then be compared.
• be confused by how probability is a measure of likelihood of an event happening. It is important to show students how several trials are needed to make frequency predictions.

Encourage students to read questions carefully as slight nuances in language are important in probability. Students whose first language is a language or dialect other than English may need particular support in this topic.

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

• We are learning to apply the language of probability to an event (likely, unlikely, even, certain, impossible).
• We are learning to calculate and record the probability of an event occurring using the number of favourable outcomes and possible outcomes.
• We are learning to explain and understand the difference between experimental and theoretical probability.

Why are we learning about this?

To explore, describe and analyse the frequency of outcomes using our knowledge of probability, given that we encounter probability in many aspects of our daily life (for example sport, weather).

What to do

Activity 1

We can measure how likely, or unlikely, it is that an event will occur using the idea of probability, which is defined using a number between 0 and 1.

Complete the following activities and record your answers in your book.

1. All the letters of the alphabet are printed on cards and put in a bag. A card is drawn out at random. The probability that the letter on the card occurs in the word ‘PERTH’ is:

a.   126

b.   526

c.  2126

2. All the letters of the word ‘AUSTRALIA’ are written on separate pieces of paper, which are placed in a box. James randomly selects a piece of paper from the box and records the letter written. What is the probability of James choosing:

a. a T?

b. an I?

c. a vowel?

3. A bag contains 10 marbles, numbered 1 to 10. One marble is removed.

a. List the sample space.

b. Write down the outcomes favourable to the event ‘a marble with an odd number is taken out’.

c. What is the probability of getting an odd number?

Activity 2

What are probabilities?

Follow the reasoning and play these fun games with a friend. Don't worry, it’s not school.

Success criteria

• I can explain the likelihood of an event happening on a scale from impossible to certain.
• I can express probability on a scale from 0 to 1.
• I can calculate and use theoretical probabilities for single and combined events using a variety of appropriate representations, including diagrams.