1. goteachmaths.co.uk Combined Events – Complete Lesson
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2. 08 December December 2018
Combined Events

3. I’m playing Monopoly and want to land on Park Lane to buy it.
I need a 7.
What is the probability I roll a 7 on 2 dice?
𝑃 7 = 1 6

4. Sample Space Diagrams
Imagine one dice was red and one was blue.
Dice 1
There are 36
equally likely outcomes. +
How many ways can
we get a 7? 2 3 4 5 6 7 8 9 10 11 12
P(7) = 6 36
= 1 6
Dice 2
1 36
P(12) =
5 36
P(6) =
Total Score

5. + 2 3 4 5 6 7 8 9 10 11 12 P(8) = P(9) = P(even) = P(0) =
Sample Space Diagrams
Dice 1
P(8) = +
P(9) = 2 3 4 5 6 7 8 9 10 11 12
P(even) =
Dice 2
P(0) =
P(more than 7) =
P(3, 5 or 10) =
Total Score

6. Answers
Sample Space Diagrams
5 36
Dice 1
P(8) = +
4 36
= 1 9
P(9) = 2 3 4 5 6 7 8 9 10 11 12
18 36
= 1 2
P(even) =
Dice 2
0 36
P(0) =
= 0
15 36
= 5 12
P(more than 7) =
9 36
= 1 4
P(3, 5 or 10) =
Total Score

8. 2 3 4 1 2 3 4 5 6 1 2 3 4 5 A student makes a hexagonal spinner (1-6)
and a pentagonal spinner (1-5).
a) Complete the Sample Space Diagram for spinning both and adding their scores.
1st Spinner 1 2 3 4 5 6 2 3 4 1 2
Calculate:
2nd Spinner 3
b) P(11) = 4
c) P(7) =
d) P(8 or more) = 5
e) P(4 or 9) =
Total Score
f) P(the same number on both spinner) =

9. A student makes a hexagonal spinner (1-6)
and a pentagonal spinner (1-5).
a) Complete the Sample Space Diagram for spinning both and adding their scores.
1st Spinner 1 2 3 4 5 6 2 3 4 5 6 7 8 9 10 11 1 2
Calculate:
2nd Spinner
1 30 3
b) P(11) =
1 6 4
c) P(7) =
1 3
d) P(8 or more) = 5
1 5
e) P(4 or 9) =
Total Score
1 6
Answers
f) P(the same number on both spinner) =

12. H, 1 T, 5 A dice and a coin are thrown at the same time.
a) Complete the Sample Space Diagram.
Dice 1 2 3 4 5 6
H, 1
T, 5
Head
Coin
Tail
b) Calculate the probability of scoring a 4 on the dice and a heads on the coin.
c) Calculate the probability of scoring tails and an odd number on the dice.
d) P(Heads and a number greater than 2) =
e) P(NOT a 5 and NOT Heads) =

13. A dice and a coin are thrown at the same time.
a) Complete the Sample Space Diagram.
Dice 1 2 3 4 5 6
H, 1
H, 2
H, 3
H, 4
H, 5
H, 6
T, 1
T, 2
T, 3
T, 4
T, 5
T, 6
Head
Coin
Tail
1 12
b) Calculate the probability of scoring a 4 on the dice and a heads on the coin.
1 4
c) Calculate the probability of scoring tails and an odd number on the dice.
1 3
d) P(Heads and a number greater than 2) =
1 3
e) P(NOT a 5 and NOT Heads) =
Answers

16. A 6-sided and a 4-sided die are thrown and
the product of their results recorded.
a) Complete a Sample Space Diagram.
b) P(Even number) =
e) P(NOT a prime number) =
c) P(less than 10) =
f) P(NOT a square number) =
d) P(NOT more than 2) =
g) P(11) =

17. Answers
A 6-sided and a 4-sided die are thrown and
the product of their results recorded.
a) Complete a Sample Space Diagram.
Dice 1 1 2 3 4 5 6 1 1 2 3 4 5 6 8 10 12 9 15 18 16 20 24 2
Dice 2 3 4
19 24
3 4
b) P(Even number) =
e) P(NOT a prime number) =
5 12
19 24
c) P(less than 10) =
f) P(NOT a square number) =
1 8
d) P(NOT more than 2) =
g) P(11) =

20. 2. 1. 3. 4.

21. Check your success! I can complete a sample space diagram.
I can use a sample space diagram to calculate combined event probabilities.
I can answer GCSE questions on
combined events.

22. Check your success! I can complete a sample space diagram.
I can use a sample space diagram to calculate combined event probabilities.
I can answer GCSE questions on
combined events.

23. Write a text message to a friend describing:
How sample space diagrams are used to find probabilities.

24. 3 4 2 5 4 3 1 5 1 2 6