  # Use Exhaustive Events

In this worksheet, students practise identifying exhaustive events and look at the probability of something not happening. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR,

Curriculum topic:   Probability

Curriculum subtopic:   Probability Combined Events and Probability Diagrams

Difficulty level:   #### Worksheet Overview

We have looked so far at finding a single probability. This time, we're going to look at exhaustive events.

What are exhaustive events?

Exhaustive events are two events that describe everything that could happen.

For example, If I throw a coin, getting a head and getting a tail are the only two things that could happen so they are exhaustive

If a roll a dice, getting a 2 and getting a 3 are not exhaustive as they don't describe everything that could happen

If I roll a dice, getting a 2 and not getting a 2 are exhaustive as they describe everything that could happen.

We know that if something is certain, it has a probability of 1.

We can use this fact to find the probability of finding the probability of something not happening.

Example: Find the probability of rolling a dice and not getting a 2

Let's look at the example from before with the dice.

The probability I get a 2 and the probability I don't get a 2 are exhaustive, this means one of them is certain to happen.  This means we can say that...

P(getting a 2) + P(not getting a 2) = 1

If we rearrange this...

P(not getting a 2) = 1 - P(getting a 2).

This means that if we know the probability of something happening, we can find the probability of it not happening.

P(not getting a 2) = 1 - 1/6 = 5/6

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