NSW Syllabuses

# Mathematics K–10 - Stage 5.1 - Statistics and Probability Probability

## Outcomes

#### A student:

• MA5.1-1WM

uses appropriate terminology, diagrams and symbols in mathematical contexts

• MA5.1-2WM

selects and uses appropriate strategies to solve problems

• MA5.1-3WM

provides reasoning to support conclusions that are appropriate to the context

• MA5.1-13SP

calculates relative frequencies to estimate probabilities of simple and compound events

Related Life Skills outcomes: MALS-38SP, MALS-39SP

## Content

• repeat a chance experiment a number of times to determine the relative frequencies of outcomes, eg using random number generators such as dice, coins, spinners or digital simulators
• recognise randomness in chance situations (Reasoning)
• recognise that probability estimates become more stable as the number of trials increases (Reasoning)
• identify theoretical probabilities as being the likelihood of outcomes occurring under ideal circumstances
• explain the relationship between the relative frequency of an event and its theoretical probability (Communicating, Reasoning)
• predict the probability of an event from experimental data using relative frequencies
• apply relative frequency to predict future experimental outcomes (Problem Solving, Reasoning)
• design a device to produce a specified relative frequency, eg a four-coloured circular spinner (Problem Solving)
• calculate probabilities of events, including events involving 'and', 'or' and 'not', from data contained in Venn diagrams representing two or three attributes, eg the Venn diagram below represents the sports played by Year 9 students

What is the probability that a randomly chosen student plays basketball or football, but not both?
• calculate probabilities of events, including events involving 'and', 'or' and 'not', from data contained in two-way tables, eg the table below represents data collected on Year 10 students comparing gender with handedness

What is the probability that a randomly chosen student is both female and right-handed?

### Background Information

Digital technologies could be used for simulation experiments to demonstrate that the relative frequency gets closer and closer to the theoretical probability as the number of trials increases.

Students may not appreciate the significance of a simulation, eg they may not transfer results from a digital simulator for tossing a die to the situation of actually tossing a die a number of times.