# Use the fact that probabilities of possible outcomes sum to 1

## Home learning focus

Understand that probabilities of possible outcomes sum to 1, and use this fact, eg when calculating the chances of winning, losing or drawing a game.

This lesson includes:

- one video
- a learning summary
- two activities with answers

# Learn

## Probability

Probability is about **estimating** or **calculating** how likely or *probable* something is to happen. It can be used to estimate the likelihood of an outcome, for example, when throwing a die or tossing a coin.

Probabilities can be written as **fractions**, **decimals** or **percentages**.

## Sum of probabilities

Consider the following facts:

1. When tossing a fair coin, the probability of obtaining a head is ½ and the probability of obtaining a tail is also ½. Adding the probabilities, you get:

½ + ½ = 1

2. Imagine you choose a letter at random from the word 'SUMS' - the probability of obtaining the letter S is ²⁄₄ (because S appears twice in the word, and there are 4 letters in total), the probability of obtaining the letter U is ¼ (because U appears once), and the probability of obtaining the letter M is also ¼, for the same reason.

Adding all these probabilities, you get:

²⁄₄ + ¼ + ¼ = 1

**The sum of the probabilities of all possible outcomes must add up to 1**. It cannot be greater or less than 1, or be a negative number.

Events that cannot occur at the same time are called **mutually exclusive** events. For example, a netball team can win, lose or draw but these things cannot take place at the same time - they are mutually exclusive. Since it is certain that one of these outcomes will happen, **their probabilities must add up to 1**.

If the probability that the netball team wins is 0.5 and the probability it draws is 0.2, then the probability of it losing must be 0.3.

Check: 0.5 + 0.2 + 0.3 = 1

Watch this short video from Pearson to learn more about probabilities of events not happening, in this case the probability of **not** selecting a certain colour of sweet.

# Practise

## Activity 1

**Quiz**

Think you know about probability? Click here to have a go at this quiz from BBC Bitesize, National 4 Maths to test your knowledge!

Question 5 requires you to note down a list of possible outcomes before working out probability - if this is something you feel less confident in, click here to learn more, and then attempt the quiz.

You can mark your answers within the quiz.

## Activity 2

**Probability and mutually exclusive events - Skills**

Keep going - try the questions in these worksheets now from Pearson to test your understanding of mutually exclusive events and that all possible outcomes of a single event must sum to 1. Write your answers on a piece of paper.

Click here for the answer sheet.

# There's more to learn

Have a look at these other resources around the BBC and the web.