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 Click on this button below to see the correct answer 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 Click this button to see if you are correct 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 Click on this button to see the correct answer 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:

Question 1
When you roll a fair dice, what is the probability that you obtain:
(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?

Question 2
A bag contains 6 red sweets and 14 blue sweets. A sweet is taken at random from the bag.
What is the probability that it is:
(a) a red sweet?
(b) a blue sweet?

Question 3
You toss a fair coin.
What is the probability that you obtain a tail?

Question 4
The diagram below shows a spinner from a game. The black arrow spins and ends up pointing to one of the four numbers.
What is the probability that the arrow points to:
(a) the number 1?
(b) an even number?
(c) a multiple of 3?

Question 5
The diagram shows a spinner that is used in a board game.
When the spinner is spun, what is the probability that it lands on:
(a) 1?
(b) 5?
(c) 4?
(d) an even number?
(e) a number less than 4?

Question 6
A bag of sweets contains 8 mints, 6 toffees and 2 boiled sweets. A sweet is taken at random from the bag.
What is the probability that it is:
(a) a mint?
(b) a toffee?
(c) a boiled sweet?
(d) not a mint?
(e) not a toffee?

Question 7
In a class there are 18 boys and 12 girls. One child is chosen at random to represent the class.
What is the probability that this child is:
(a) a girl?
(b) a boy?

Question 8
The diagram shows a piece of card that is folded to form a dice.
When the dice is rolled, what is the probability that it shows:
(a) a blue face?
(b) a red face?
(c) a yellow face?
(d) a face that is not red?
(e) a face that is not yellow?

Question 9
The children in a class were asked to name their favourite colour. The results are given in the table below.
If a child is picked at random from the class, what is the probability that their favourite colour is:
(a) red?
(b) yellow?
(c) pink?
(d) black?
(e) not pink?
(f) not green?

Question 10
A bag contains 6 red balls and some white balls. When a ball is chosen at random, the probability that it is red is .
How many white balls are in the bag?


You have now completed Unit 21 Section 2
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Produced by A.J.Reynolds January 2001