This document is a presentation on probability of two or more events. It includes sections on probability outcomes for rolling a dice and flipping a coin simultaneously, rolling two dice and adding the scores, using tree diagrams to calculate probabilities of outcomes from rolling two dice or drawing balls from containers. It also addresses common misconceptions about probability, such as assuming the number of possible outcomes corresponds to the probability of a specific outcome, or that order matters in independent events. The presentation provides examples and prompts users to complete probability calculations to demonstrate their understanding of fundamental probability concepts involving two or more random events.

1. Unit 20
Probability of Two or More Events
Presentation 1 A Coin and a Dice
Presentation 2 Two Dice
Presentation 3 Tree Diagrams for Two Dice
Presentation 4 Tree Diagrams for Coloured Balls
Presentation 5 Misconceptions

2. Unit 20
Probability of Two or More Events
A Coin and a Dice

3. A fair dice is rolled and an unbiased coin is tossed at the same time.
Complete the following table to show the possible outcomes:
How many outcomes are there:
a) in total
b) that include a 6
c) that include a head
d) that include an even number
1 2 3 4 5 6
H
T
H1 H2 H3 H4 H5 H6
T1 T2 T3 T4 T5 T6
12
2
6
6

4. Unit 20
Probability of Two or More Events
You have finished viewing:
A Coin and a Dice
Return to front slide
Presentation 1 A Coin and a Dice
Presentation 2 Two Dice
Presentation 3 Tree Diagrams for Two Dice
Presentation 4 Tree Diagrams for Coloured Balls
Presentation 5 Misconceptions

5. Unit 20
Probability of Two or More Events
Two Dice

6. Complete the following table to show the possible outcomes when the two
dice are thrown at the same time and their scores added:
How many outcomes are there:
a) in total
b) that give a score of 9
c) that give a score of 6
d) that give a score of 12
1 2 3 4 5 6
1
2
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
3
4
5
6
36
4
5
1

7. The table shows the possible outcomes when two fair dice are thrown and
their scores added
What is the probability of getting a score:
a) of 9
b) of 10
c) less than 6
d) more than 9
1 2 3 4 5 6
1
2
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
3
4
5
6

8. Unit 20
Probability of Two or More Events
You have finished viewing:
Two Dice
Return to front slide
Presentation 1 A Coin and a Dice
Presentation 2 Two Dice
Presentation 3 Tree Diagrams for Two Dice
Presentation 4 Tree Diagrams for Coloured Balls
Presentation 5 Misconceptions

9. Unit 20
Probability of Two or More Events
Tree Diagrams for Two Dice

10. Complete the tree diagram and use it to determine the probability of
getting:
a)2 sixes, b) 1 six, c) no sixes,
when you roll two fair dice
Six
Not Six
OUTCOMES PROBABILITIES
Six, SixSix, Six
Six, Not SixSix, Not Six
Not Six, SixNot Six, Six
Not Six, Not SixNot Six, Not Six
Six
Six
Not Six
Not Six

11. a)p (2 sixes) =
b)p (1 six) =
c)p (no sixes) =
Six
Not Six
OUTCOMES PROBABILITIES
Six, SixSix, Six
Six, Not SixSix, Not Six
Not Six, SixNot Six, Six
Not Six, Not SixNot Six, Not Six
Six
Six
Not Six
Not Six
+ =

12. Unit 20
Probability of Two or More Events
You have finished viewing:
Tree Diagrams for Two Dice
Return to front slide
Presentation 1 A Coin and a Dice
Presentation 2 Two Dice
Presentation 3 Tree Diagrams for Two Dice
Presentation 4 Tree Diagrams for Coloured Balls
Presentation 5 Misconceptions

13. Unit 20
Probability of Two or More Events
Tree Diagrams for Coloured Balls

14. There are 5 yellow balls (Y) and 4 green balls (G) in a container. One ball
is taken out at random then put back. A second ball is then taken out at
random. Complete the tree diagram:
Y
G
OUTCOMES PROBABILITIES
Y, YY, Y
Y, GY, G
G, YG, Y
G, GG, G
Y
Y
G
G

15. Determine:
a)p (2 yellow balls) =
b)p (2 green balls) =
c)p (1 green and 1 yellow) =
Y
G
OUTCOMES PROBABILITIES
Y, YY, Y
Y, GY, G
G, YG, Y
G, GG, G
Y
Y
G
G
+ =

16. There are 5 yellow balls (Y) and 4 green balls (G) in a container. One ball
is taken out at random but NOT put back in. A second ball is then taken
out at random. Complete the tree diagram:
Y
G
OUTCOMES PROBABILITIES
Y, YY, Y
Y, GY, G
G, YG, Y
G, GG, G
Y
Y
G
G

17. Determine:
a)p (2 yellow balls) =
b)p (2 green balls) =
c)p (1 green and 1 yellow) =
Y
G
OUTCOMES PROBABILITIES
Y, YY, Y
Y, GY, G
G, YG, Y
G, GG, G
Y
Y
G
G
+ =

18. Unit 20
Probability of Two or More Events
You have finished viewing:
Tree Diagrams for Coloured Balls
Return to front slide
Presentation 1 A Coin and a Dice
Presentation 2 Two Dice
Presentation 3 Tree Diagrams for Two Dice
Presentation 4 Tree Diagrams for Coloured Balls
Presentation 5 Misconceptions

19. Unit 20
Probability of Two or More Events
Miconceptions

20. Each of the following is a misconception (incorrect statement). Explain
why.
Misconception 1
When two fair dice are rolled and
the numbers thrown are added,
the probability of getting a total of
6 is because there are 11
different possible outcomes.
Misconception 1
When two fair dice are rolled and
the numbers thrown are added,
the probability of getting a total of
6 is because there are 11
different possible outcomes.
Misconception 2
If six fair dice are thrown at the
same time, you are less likely to
obtain:
1, 1, 1, 1, 1, 1 than
1, 2, 3, 4, 5, 6
Misconception 2
If six fair dice are thrown at the
same time, you are less likely to
obtain:
1, 1, 1, 1, 1, 1 than
1, 2, 3, 4, 5, 6
Misconception 3
If you choose 1 ball from each box, you are more
likely t obtain a black ball from box A than from box B,
because there are more black balls in box A.
Box A Box B
Misconception 4
You spin two unbiased
coins. The probability of
getting a HEAD and a
TAILS is because you
can get:
•2 HEADS
•1 HEAD and 1 TAIL
•2 TAILS

21. Unit 20
Probability of Two or More Events
You have finished viewing:
Misconceptions
Return to front slide
Presentation 1 A Coin and a Dice
Presentation 2 Two Dice
Presentation 3 Tree Diagrams for Two Dice
Presentation 4 Tree Diagrams for Coloured Balls
Presentation 5 Misconceptions