What is the notation for the probability of event A not occurring?

The notation for the probability of event A not occurring is \( P(A') \) or \( P(\text{not } A) \).

In probability, when we talk about the likelihood of an event not happening, we use specific notation to make it clear. If we have an event A, the probability that A does not occur is denoted as \( P(A') \) or sometimes \( P(\text{not } A) \). This is known as the complement of event A.

The complement rule in probability states that the sum of the probabilities of an event and its complement is always 1. Mathematically, this is expressed as \( P(A) + P(A') = 1 \). This means if you know the probability of event A occurring, you can easily find the probability of it not occurring by subtracting \( P(A) \) from 1. For example, if the probability of it raining tomorrow (event A) is 0.3, then the probability of it not raining (event A') is \( 1 - 0.3 = 0.7 \).

Understanding this concept is crucial because it helps in solving various probability problems. For instance, if you are given the probability of an event happening and need to find the probability of it not happening, you can use the complement rule. This notation and rule are fundamental in probability theory and are widely used in different types of probability questions you might encounter in your GCSE Maths exams.