---
title: "Complementary events"
description: "Understand and apply the rule that probabilities of all mutually exclusive outcomes sum to one; use this to find the probability of a complementary event (P(not A) = 1 − P(A))"
canonical: https://lightmysky.com/learn/mathematics/complementary-events-mt_XfyqXLqzpx
source: https://lightmysky.com/learn/mathematics/complementary-events-mt_XfyqXLqzpx.md
retrieved: 2026-10-19
---

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# Complementary events

Understand and apply the rule that probabilities of all mutually exclusive outcomes sum to one; use this to find the probability of a complementary event (P(not A) = 1 − P(A))

Subject: Mathematics · Area: Probability · Ages 11 to 13
Page: https://lightmysky.com/learn/mathematics/complementary-events-mt_XfyqXLqzpx

## Ready when they can

- Verify that probabilities of all outcomes listed for a spinner sum to 1
- Calculate the probability of NOT rolling a 6 as 1 − 1/6 = 5/6
- Identify an error in a probability distribution where the values do not sum to 1

## Lesson: Complementary events

You already know that all the probabilities in a situation add up to 1. That fact lets you find the chance of not rolling a 6 without listing the other five faces. If A is one event, 'not A' means everything else that could happen instead. A and 'not A' always add up to 1, the top of the probability scale. That gives the rule P(not A) = 1 − P(A): take P(A) away from 1.

*(drawing: Three marbles out of eight are red. The other five marbles are 'not red', so P(not red) = 5/8.)*

**Example.** A spinner has three sections. One has a probability of 0.45, and the next has 0.25. All three probabilities must add up to 1, so the third section is 1 − 0.45 − 0.25 = 0.3.

**Tip.** Once you know P(A), you can find P(not A) with 1 − P(A). You don't need to know anything else about the situation.

**Recap.** P(not A) = 1 − P(A), because A and everything else always add up to 1.

## Practice

20 questions on this page, each with its working shown.

## Needs first

- [Probabilities Sum to One](https://lightmysky.com/learn/mathematics/probabilities-sum-to-one-mt_3fwYu7imd4)
- [The Probability Scale](https://lightmysky.com/learn/mathematics/the-probability-scale-mt_vmQJAtAFuy)

## Opens up

- [Sets & Venn Diagrams](https://lightmysky.com/learn/mathematics/sets-and-venn-diagrams-mt_1YwOCMMwD8)