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



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.

Pearson - The probability that something will not happen


Activity 1


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.

Mutually exclusive events

Click here for the answer sheet.

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

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