AC9M8P01

See also: Learning Areas / Mathematics / Mathematics / Probability / Year 8

recognise that complementary events have a combined probability of one; use this relationship to calculate probabilities in applied contexts

Elaborations

• AC9M8P01_E1 - understanding that knowing the probability of an event allows the probability of its complement to be found, including for those events that are not equally likely, such as getting a specific novelty toy in a supermarket promotion
• AC9M8P01_E2 - using the relationship that for a single event \(A\), \(Pr(A)+Pr(\;not\;A)\;=\;1\); for example, if the probability that it rains on a particular day is \(80\%\), the probability that it does not rain on that day is \(20\%\), or the probability of not getting a \(6\) on a single roll of a fair dice is \(1-\frac16=\frac56\)
• AC9M8P01_E3 - using the sum of probabilities to solve problems, such as the probability of starting a game by throwing a \(5\) or \(6\) on a dice is \(\frac13\) and probability of not throwing a \(5\) or \(6\) is \(\frac23\)

Achievement Standard Components

• ASMAT819 - Students represent the possible combinations of 2 events with tables and diagrams, and determine related probabilities to solve practical problems.
• ASMAT820 - They conduct experiments and simulations using digital tools to determine related probabilities of compound events.