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Mathematics / Year 8 / Probability
Curriculum content descriptions
recognise that complementary events have a combined probability of one; use this relationship to calculate probabilities in applied contexts (AC9M8P01)
Elaborations
- 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
- 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 \(1-\frac16=\frac56\)
- 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 \(\frac23\)
- 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
General capabilities
ScOT terms
Complementary events, Expected frequency