Understanding chance description
Our modern understandings of probability date from the second half of the 17th century with the analysis of games of chance. Many of the basic ideas of probability can run contrary to common beliefs. Recognising how what has happened in the past does not influence what will happen in the future with independent events often needs people to overcome strongly held beliefs. This sub-element describes how a student becomes increasingly able to use the language of chance and the numerical values of probabilities when determining the likelihood of an event. Understanding chance is often essential to interpret data.
Some students will communicate using augmentative and alternative communication strategies to demonstrate their numeracy skills. This may include digital technologies, sign language, braille, real objects, photographs and pictographs.
Each sub-element level has been identified by upper-case initials and in some cases lower-case letters of the sub-element name followed by ascending numbers. The abbreviation for this sub-element is UnC. The listing of indicators within each level is non-hierarchical. Subheadings have been included to group related indicators. Where appropriate, examples have been provided in brackets following an indicator.
UnC1
Describing chance
- describes everyday occurrences that involve chance
- recognises that some events might or might not happen
- makes predictions on the likelihood of simple, everyday occurrences
UnC2
Comparing chance
- explains why one result is more likely than another (if there are more blue than red marbles in a bag, blue is more likely to be selected)
- explains why outcomes of chance experiments may differ from expected results
UnC3
Fairness
- identifies all possible outcomes from simple experiments
- explains that 'fairness' of chance outcomes is related to the equal likelihood of all possible outcomes
- identifies unfair elements in games that affect the chances of winning (having an unequal number of turns)
- recognises that all probabilities must lie between impossible (no chance) and certain
UnC4
Probabilities
- expresses probability as the number of ways an event can happen out of the total number of possibilities
- describes probabilities as fractions of one (the probability of an even number when rolling a dice is \(\frac12\))
UnC5
Calculating probabilities
- describes the likelihood of events using a fraction or percentage
- interprets the odds of an event (odds of 5:1, the odds against rolling a 6, means a wager of $1 stands to win $5)
- explains how probability is not affected by previous results (If a coin is tossed and heads have come up 7 times in a row, it is still equally likely that the next toss will be heads or tails)
- recognises that the chance of something occurring or not occurring has a total probability of 1 (the probability of rolling a 3 is \(\frac16\) and the probability of not rolling a 3 is \(\frac56\))
- determines the probability of compound events (tossing 2 coins)
- compares expected and actual results of a chance event