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.

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

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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