Complementary Events

The complement of an event is everything in the sample space that is not in the event. In NSW Year 8 maths (NESA outcome MA4‑PRO‑C‑01) the two probabilities always add to 1, so \(P(\text{not A}) = 1 - P(\text{A})\).

You will use this rule with fractions, decimals and percentages, such as a train that runs on time with probability 0.93, and check whether two events really are complementary when a draw is possible. You will also use the rule as a counting shortcut, find the chance of neither of two events, work out the expected number of seeds that sprout and find a missing probability in a table. It is part of Year 8 Probability.