AC9M8P01 Year 8 Mathematics

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

Elaborations

• • Elaboration 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
• • Elaboration 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 1-1/6=5/6
• • Elaboration 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 1/3 and probability of not throwing a 5 or 6 is 2/3
• • Elaboration investigating how various applications of artificial intelligence use the probability of complementary events when assessing the likelihood of favourable and unfavourable outcomes and making informed decisions based on these probabilities; for example, in binary classification problems where data is classified into one of two categories, such as spam or not spam, fraud or not fraud