Unit 21 Section 2 : Probability of a Single Event

In this section we will look at how we calculate the probabilities of single events.

Probabilities are always between 0 and 1, and can be written as fractions, decimals or percentages.
In this section we will write all probabilities as fractions.

We are only going to look at cases where all the possible outcomes are equally likely, like rolling a fair dice.
On a fair or unbiased dice, the six possible outcomes each have the same chance of occuring - they are equally likely.

The words "fair" or "unbiased" mean that all outcomes are equally likely.

To find the probability of a particular event, we use this formula:

Example 1
Imagine we are rolling a fair dice. There are six equally likely outcomes: 1, 2, 3, 4, 5 and 6.

(a) What is the probability of getting a five?
In this case there is only one successful outcome, 5.

(b) What is the probability of getting an even number?
In this case there are 3 successful outcomes, which are 2, 4 and 6.

(c) What is the probability of getting a four or a five?
In this case there are 2 successful outcomes, which are 4 and 5.

Notice that we simplify the fractions in the answers where it is possible to do so.

Example 2
A bag of sweets contains 6 mints and 4 eclairs. One sweet is taken at random from the bag.
In this case there are ten equally-likely outcomes: six mints and four eclairs.

(a) What is the probability of picking a mint?
As there are six mints in the bag, there are six successful outcomes.

(b) What is the probability of picking an eclair?
As there are four eclairs, there are four successful outcomes.

Practice Questions

Work out the answer to the questions below then click

to see whether you are correct.

(1) A spinner with five equally likely outcomes is spun. The outcomes are 1, 2, 3, 4 and 5.
(a) What is the probability of getting a two?

(b) What is the probability of getting an even number?

(2) The spinner is now altered to show the numbers 1, 2, 2, 2 and 4.
(a) What is the new probability of getting a two?

(b) What is the new probability of getting an even number?

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the

button to find out whether you have answered correctly. If you are right then

will appear and you should move on to the next question. If

appears then your answer is wrong. Click on

to clear your original answer and have another go. If you can't work out the right answer then click on

to see the answer.

Most of the answers in this section are fractions. Each fraction has two input boxes.
Put the numerator in the top box and the denominator in the bottom box, like this:

You have now completed Unit 21 Section 2

Your overall score for this section is

Correct Answers
You answered questions correctly out of the questions in this section.

Incorrect Answers
There were questions where you used the Tell Me button.
There were questions with wrong answers.
There were questions you didn't attempt.

Since these pages are under development, we find any feedback extremely valuable. Click here to fill out a very short form which allows you make comments about the page, or simply confirm that everything works correctly.
Return to the Tutorials Menu

Produced by A.J.Reynolds January 2001


(a) an odd number?



(b) a multiple of 3?



(c) a 2?



(d) a number less than 5?



(e) a number greater than 4?



(f) a 3 or a number less than 3?

(a) a mint?



(b) a toffee?



(c) a boiled sweet?



(d) not a mint?



(e) not a toffee?

(a) a girl?



(b) a boy?