Dice Probability
1) Two fair dice are thrown and the
scores are ADDED together.
• Complete the sample space diagram
• How many outcomes are there?
• What is the probability of getting
a score of ‘5’?
• What is the probability of getting
a score greater than ‘9’?
• What is the probability of getting
a score less than ‘7’?
2 3 4 5 6 7
3 4 5 6 7 8
4 5 6 7 8 9
5 6 7 8 9 10
6 7 8 9 10 11
7 8 9 10 11 12
2) Two fair dice are thrown and the
scores are MULTIPLIED together.
• Complete the sample space diagram
• How many outcomes are there?
• What is the probability of getting
a score of ‘6’?
• What is the probability of getting
a score greater than ‘16’?
• What is the probability of getting
a score less than ‘4’?
1 2 3 4 5 6
2 4 6 8 10 12
3 6 9 12 15 18
4 8 12 16 20 24
5 10 15 20 25 30
6 12 18 24 30 36
3) A six-faced dice and a four-faced
dice are thrown. The first score is
SUBTRACTED FROM the second
score.
• Complete the sample space diagram
• How many outcomes are there?
• What is the probability of getting
a negative score?
• What is the probability of getting
a score ≥ 0?
First Score
Second Score
0 -1 -2 -3 -4 -5
1 0 -1 -2 -3 -4
2 1 0 -1 -2 -3
3 2 1 0 -1 -2
36
36
24
4
36
=
1
9
4
36
=
1
9
6
36
=
1
6
10
36
=
5
18
10
24
=
5
12
14
24
=
7
12
15
36
=
5
12
5
36
7.SP.C.8.B
©Visual Maths Resources
www.cazoommaths.com/us
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Sample Space Tree Diagrams
ANSWERS
Section A
1) Jamie has two fair spinners.
One has three equal sections colored red,
blue and yellow. The other has four equal
sections numbered 1, 2, 3 and 4. Jamie spins
both spinners.
Complete the sample space diagram.
Yellow
Red
Blue
1
3
2
4
B
B B B Y Y Y Y R R R R
Number
1
2 3 4 1 2 3 4 1 2 3 4
2) A fair dice and a coin are thrown together.
a. Draw a sample space diagram to represent the possible outcomes.
b. What is the probability of getting an even number and a tails?
3) A game is played using the counters inside two bags.
Bag 1 contains a green, purple and an orange counter.
Bag 2 contains 3 counters with the numbers 4, 5 and 6 on them.
a. Draw a sample space diagram to show all the possible outcomes when one
counter is taken from each bag.
b. What is probability of someone picking a green counter and the number 4?
c. Find the probability of taking an orange counter and a number greater than 4.
1 2 3 4 5 6
H H1 H2 H3 H4 H5 H6
T T1 T2 T3 T4 T5 T6
Green Purple Orange
4 G4 P4 O4
5 G5 P5 O5
6 G6 P6 O6
3
12
=
1
4
1
9
2
9
7.SP.C.8.B
©Visual Maths Resources
www.cazoommaths.com/us
6WDWLVWLFV3UREDELOLW\ - 3UREDELOLW\
Sample Space Tree Diagrams
ANSWERS
Section B
Color