# Introduction to Probability

How likely is it that’ll you’ll understand probability by the end of this post? We’d hope, ‘likely’ to ‘certain’! Positioned as an introduction to probability, you’ll find an easy-to-read breakdown of the basics supported by a range of questions that you can try out for yourself.

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Probability measures how likely an event is to happen. Probabilities can be described in words. They can also be described using fractions and decimals between 0 and 1 or percentages between 0 and 100%. We never use ratios to represent a probability.

## The Probability Scale

If an event is impossible, its probability is 0. If it is certain then its probability is 1 or 100%. The probability scale includes all the options between these two events.

### Example 1

A fair six-sided dice is thrown. What is the probability that the score is 5?

The dice has six faces numbered 1-6 inclusive. This means that there is only one way that a score of 5 can occur and the total number of outcomes is six. We can use P( ) to represent the probability of something occurring.

• P(scoring a 5) = $\frac{1}{6}$

#### Probability of an Event Not Occurring

If events cannot occur together, we say that they are mutually exclusive. If this is the case, we say that the sum of the probabilities is 1.

### Example 2

The probability that a goldfish measures less than 4cm is 0.7. What is the probability that a goldfish measures 4cm or more?

• P(goldfish measure 4cm or more) = $1 - 0.7 = 0.3$
• *as the sum of the probabilities has to be 1.

Let’s not leave it all to chance, eh? Increase the likelihood of understanding the content material with this Introduction to Probability KS3 Walkthrough Worksheet.

### Introduction to Probability Questions – Now It’s Your Turn…

1. Match up the events with the likelihood of them occurring.

2. A fair three-sided spinner is marked with the numbers 1, 2 and 3. The spinner is spun. Draw your own probability scale (like below) and mark the probability that the spinner lands on 3.

3. A bag contains 4 blue counters and 1 red counter. A counter is drawn at random. Draw your own probability scale and mark the probability that the counter is red.

4. A fair six-sided dice is thrown. What is the probability that the dice lands on an even number? Give your answer as a fraction in its simplest form.

5. In a class of 30 students, 7 students only have a cat and 8 students only have a dog. A student is chosen at random. What is the probability that the student only has a cat?

6. A bag contains 4 blue counters, 5 red counters and 1 green counter. A counter is chosen at random. Find the probability that the counter is blue, giving your answer as a decimal.

7. In a group of men, the probability that a man is taller than 1.85m is 0.03. What is the probability that a man chosen at random is not taller than 1.85m?

8. A bead is chosen at random from a bag. The probability of choosing a red bead is 1/5. What is the probability of choosing a bead that is not red?

9. A bag of sweets contains toffees, gummies and sherbet lemons only. A sweet is chosen at random. The probability of choosing a toffee is 0.3 and the probability of choosing a gummy is 0.25. What is the probability of choosing a sherbet lemon?

10. A spinner is spun. It can land on 1, 2, 3 or 4. The table shows the probabilities of the spinner landing on each number. Fill in the missing value.

1. 2. 3. 4. $\frac{3}{6} = \frac{1}{2}$
5. $\frac{7}{30}$
6. $4 + 5 + 1 = 10$ $\frac{4}{10} = 0.4$
7. $1 - 0.03 = 0.97$
8. $1 - \frac{1}{5} = \frac{4}{5}$
9. $0.3 + 0.25 = 0.55$ $1 - 0.55 = 0.45$
10. $0.2 + 0.15 + 0.4 = 0.75$ $1 - 0.75 = 0.25$

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