Australian Curriculum Mathematics/Mathematical Methods/Counting and Probability

Australian Curriculum ContentSource: Australian Curriculum, Assessment and Reporting Authority (ACARA), downloaded from the Australian Curriculum website on (5 October 2015). Combinations understand the notion of a combination as an unordered set of r objects taken from a set of n distinct objects use the notation (nr) and the formula (nr)=n!/(n−r)! for the number of combinations of r objects taken from a set of n distinct objects expand (x+y)^n for small positive integers n recognise the numbers (nr) as binomial coefficients, (as coefficients in the expansion of (x+y)^n) use Pascal’s triangle and its properties. Language of events and sets review the concepts and language of outcomes, sample spaces and events as sets of outcomes use set language and notation for events, including A¯¯¯ (or A') for the complement of an event A, A∩B for the intersection of events A and B, and A?B for the union, and recognise mutually exclusive events use everyday occurrences to illustrate set descriptions and representations of events, and set operations. Review of the fundamentals of probability review probability as a measure of ‘the likelihood of occurrence’ of an event review the probability scale: 0≤P(A)≤1 for each event A, with P(A)=0 if A is an impossibility and P(A)=1 if A is a certainty review the rules: P(A¯¯¯)=1−P(A) and P(A∪B)=P(A)+P(B)−P(A∩B) use relative frequencies obtained from data as point estimates of probabilities. Conditional probability and independence understand the notion of a conditional probability and recognise and use language that indicates conditionality use the notation P(A|B) and the formula P(A∩B)=P(A|B)P(B) understand the notion of independence of an event A from an event B, as defined by P(A|B)=P(A) establish and use the formula P(A∩B)=P(A)P(B) for independent events A and B, and recognise the symmetry of independence use relative frequencies obtained from data as point estimates of conditional probabilities and as indications of possible independence of events. __TOC__ References