Key Stage 3 (KS3) · Mathematics

Sample Spaces: Practice Questions

3 multiple-choice questions marked as you go, and 4 written questions with worked solutions. All on Sample Spaces.

7 questions16 marksFree, no account

Question 1

1 mark

A bag contains three balls of different colours: red (R), green (G), and blue (B). Two balls are drawn one after another with replacement. Which of the following sets correctly represents the sample space of this experiment?

Question 2

1 mark

A fair six-sided die is rolled twice. Let \( S \) be the sample space of all possible outcomes. Let event \( A \) be the event that the sum of the two numbers is a prime number, and event \( B \) be the event that the product of the two numbers is a multiple of 4. Find the number of outcomes in the set \( A \cap B \).

Question 3

1 mark

Two fair coins are tossed simultaneously. What is the total number of outcomes in the sample space?

Question 4

2 marks

A fair six-sided die is rolled once. Find the probability of obtaining a prime number. List the sample space first.

Write your answer out first, then check it against the worked solution.

Question 5

4 marks

Two fair coins are tossed at the same time. Using a tree diagram or a list, determine the sample space and find the probability of obtaining at least one Head.

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Question 6

2 marks

A spinner is divided into four equal sectors colored Red, Blue, Yellow, and Green. List the sample space of the outcomes when the spinner is spun once.

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Question 7

5 marks

Two fair four-sided dice (numbered 1 to 4) are rolled.
(a) List all possible outcomes in the sample space using a table or coordinates.
(b) Find the probability that the sum of the two dice is 5.

Write your answer out first, then check it against the worked solution.

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