represents probabilities of simple and compound events
TEACHING POINTS
Probability is concerned with the level of certainty that a particular event will occur. The higher the probability of an event, the ‘more certain’ or ‘more likely’ it is that the event will occur.
Probability is used widely by governments and in many fields, including mathematics, statistics, science, business and economics.
In everyday situations, probabilities are key to such areas as risk assessment, finance, and the reliability of products such as cars and electronic goods.
It is therefore important across society that probabilities are understood and used appropriately in decision making.
LANGUAGE
A simple event has outcomes that are equally likely. In a chance experiment, such as rolling a standard six-sided die once, an event might be one of the outcomes or a collection of the outcomes. For example, an event might be that an odd number is rolled, with the favourable outcomes being a ‘1’, a ‘3’ and a ‘5’.
It is important that students learn the correct terminology associated with probability.
Expectations of Attainment
Construct sample spaces for single-step experiments with equally likely outcomes (ACMSP167)
use the term ‘chance experiment’ when referring to actions such as tossing a coin, rolling a die, or randomly selecting an object from a bag
use the term ‘outcome’ to describe a possible result of a chance experiment and list all of the possible outcomes for a single-step experiment
use the term ‘sample space’ to describe a list of all of the possible outcomes for a chance experiment, eg if a standard six-sided die is rolled once, the sample space is {1,2,3,4,5,6}
distinguish between equally likely outcomes and outcomes that are not equally likely in single-step chance experimentsLiteracy
describe single-step chance experiments in which the outcomes are equally likely, eg the outcomes for a single toss of a fair coin (Communicating, Reasoning)
describe single-step chance experiments in which the outcomes are not equally likely, eg the outcomes for a single roll of a die with six faces labelled 1, 2, 3, 4, 4, 4 are not equally likely since the outcome ‘4’ is three times more likely to occur than any other outcome (Communicating, Reasoning)Critical and creative thinking
design a spinner, given the relationships between the likelihood of each outcome, eg design a spinner with three colours, red, white and blue, so that red is twice as likely to occur as blue, and blue is three times more likely to occur than white (Problem Solving)
Assign probabilities to the outcomes of events and determine probabilities for events (ACMSP168)
use the term ‘event’ to describe either one outcome or a collection of outcomes in the sample space of a chance experiment, eg in the experiment of rolling a standard six-sided die once, obtaining the number ‘1’ is an ‘event’ and obtaining a number divisible by three is also an eventLiteracy
explain the difference between experiments, events, outcomes and the sample space in chance situations (Communicating)
assign a probability of 0 to events that are impossible and a probability of 1 to events that are certain to occurLiteracy
explain the meaning of the probabilities 0, 12 and 1 in a given chance situation (Communicating)
assign probabilities to simple events by reasoning about equally likely outcomes, eg the probability of randomly drawing a card of the diamond suit from a standard pack of 52 playing cards is 1352=14
express the probability of an event, given a finite number of equally likely outcomes in the sample space, as P(event)=number of favourable outcomestotal number of outcomesLiteracy
interpret and use probabilities expressed as fractions, percentages or decimals (Communicating, Reasoning)
solve probability problems involving single-step experiments using cards, dice, spinners, etc
establish that the sum of the probabilities of all of the possible outcomes of a single-step experiment is 1
identify and describe the complement of an event, eg the complement of the event ‘rolling a 6’ when rolling a die is ‘not rolling a 6’
establish that the sum of the probability of an event and its complement is 1, ie P(event)+P(complement of event)=1
calculate the probability of a complementary event using the fact that the sum of the probabilities of complementary events is 1, eg the probability of ‘rolling a 6’ when rolling a die is 16, therefore the probability of the complementary event, ‘not rolling a 6’, is 1−16=56
