# Sample Space Diagrams

In this worksheet, students use the outcomes shown in sample space diagrams to answer probability questions.

Key stage:  KS 4

Curriculum topic:  Probability

Curriculum subtopic:  Calculate the Probability of Independent and Dependent Combined Events

Difficulty level:

### QUESTION 1 of 10

A sample space diagram is simply a diagram that helps you display outcomes in a logical and clear way. When two events take place, there are a number of possible outcomes.

Example

Two dice are thrown and the results are shown in this sample space diagram.

What is the probability that the two dice will show different numbers?

The sample space diagram shows that there are 6 x 6 = 36 outcomes in total.

The ones showing doubles are shaded. There are 6 of these, and so 36 - 6 = 30 where the numbers are different.

P(different numbers) = 30/36 = 5/6

Two dice are thrown and the results are shown in this sample space diagram.

What is the probability that the two dice will show the same numbers?

(Write your answer as a fraction in the form a/b in its lowest terms)

Two dice are thrown and the results are shown in this sample space diagram.

What is the probability that the two dice will both show even numbers?

(Write your answer as a fraction in the form a/b in its lowest terms)

Two dice are thrown and the results are shown in this sample space diagram.

What is the probability that the two dice will both show odd numbers?

(Write your answer as a fraction in the form a/b in its lowest terms)

Two dice are thrown and the results are shown in this sample space diagram.

What is the probability that the two dice will both show one even number and one odd number?

(Write your answer as a fraction in the form a/b in its lowest terms)

Two dice are thrown and the results are shown in this sample space diagram.

What is the probability that the two dice will both show prime numbers?

(Write your answer as a fraction in the form a/b in its lowest terms)

Two tetrahedral dice are thrown. Each is numbered from 1 to 4.

Draw a sample space diagram to show all the possible outcomes.

How many outcomes are there?

Two tetrahedral dice are thrown. Each is numbered from 1 to 4.

What is the probability that the two dice will both show the same numbers?

(Write your answer as a fraction in the form a/b in its lowest terms)

Two tetrahedral dice are thrown. Each is numbered from 1 to 4.

What is the probability that the two dice will show different numbers?

(Write your answer as a fraction in the form a/b in its lowest terms)

Two tetrahedral dice are thrown. Each is numbered from 1 to 4.

What is the probability that the two dice will both show even numbers?

(Write your answer as a fraction in the form a/b in its lowest terms)

Two tetrahedral dice are thrown. Each is numbered from 1 to 4.

What is the probability that at least one die will show a 4?

(Write your answer as a fraction in the form a/b in its lowest terms)

• Question 1

Two dice are thrown and the results are shown in this sample space diagram.

What is the probability that the two dice will show the same numbers?

(Write your answer as a fraction in the form a/b in its lowest terms)

1/6
EDDIE SAYS
6/36
• Question 2

Two dice are thrown and the results are shown in this sample space diagram.

What is the probability that the two dice will both show even numbers?

(Write your answer as a fraction in the form a/b in its lowest terms)

1/4
EDDIE SAYS
9/36
• Question 3

Two dice are thrown and the results are shown in this sample space diagram.

What is the probability that the two dice will both show odd numbers?

(Write your answer as a fraction in the form a/b in its lowest terms)

1/4
EDDIE SAYS
9/36
• Question 4

Two dice are thrown and the results are shown in this sample space diagram.

What is the probability that the two dice will both show one even number and one odd number?

(Write your answer as a fraction in the form a/b in its lowest terms)

1/2
EDDIE SAYS
18/36
• Question 5

Two dice are thrown and the results are shown in this sample space diagram.

What is the probability that the two dice will both show prime numbers?

(Write your answer as a fraction in the form a/b in its lowest terms)

1/4
EDDIE SAYS
9/36
• Question 6

Two tetrahedral dice are thrown. Each is numbered from 1 to 4.

Draw a sample space diagram to show all the possible outcomes.

How many outcomes are there?

16
EDDIE SAYS
4 × 4
• Question 7

Two tetrahedral dice are thrown. Each is numbered from 1 to 4.

What is the probability that the two dice will both show the same numbers?

(Write your answer as a fraction in the form a/b in its lowest terms)

1/4
EDDIE SAYS
4/16
• Question 8

Two tetrahedral dice are thrown. Each is numbered from 1 to 4.

What is the probability that the two dice will show different numbers?

(Write your answer as a fraction in the form a/b in its lowest terms)

3/4
EDDIE SAYS
12/16
• Question 9

Two tetrahedral dice are thrown. Each is numbered from 1 to 4.

What is the probability that the two dice will both show even numbers?

(Write your answer as a fraction in the form a/b in its lowest terms)

1/4
EDDIE SAYS
4/16
• Question 10

Two tetrahedral dice are thrown. Each is numbered from 1 to 4.

What is the probability that at least one die will show a 4?

(Write your answer as a fraction in the form a/b in its lowest terms)