1. Definitions
Probability

2. Definitions
Probability
Probability:the chance of something happening

3. Definitions
Probability
Probability:the chance of something happening
Sample Space:all possible outcomes

4. Definitions
Probability
Probability:the chance of something happening
Sample Space:all possible outcomes
Equally Likely Events:events which have an equal chance of
happening

5. Definitions
Probability
Probability:the chance of something happening
Sample Space:all possible outcomes
Equally Likely Events:events which have an equal chance of
happening
Mutually Exclusive Events:only one possible outcome can occur at
any one time.

6. Definitions
Probability
Probability:the chance of something happening
Sample Space:all possible outcomes
Equally Likely Events:events which have an equal chance of
happening
Mutually Exclusive Events:only one possible outcome can occur at
any one time.
e.g. a coin can be either a head or a tail, not both

7. Definitions
Probability
Probability:the chance of something happening
Sample Space:all possible outcomes
Equally Likely Events:events which have an equal chance of
happening
Mutually Exclusive Events:only one possible outcome can occur at
any one time.
e.g. a coin can be either a head or a tail, not both
Non-Mutually Exclusive Events:more than one outcome could
possibly happen at any one time

8. Definitions
Probability
Probability:the chance of something happening
Sample Space:all possible outcomes
Equally Likely Events:events which have an equal chance of
happening
Mutually Exclusive Events:only one possible outcome can occur at
any one time.
e.g. a coin can be either a head or a tail, not both
Non-Mutually Exclusive Events:more than one outcome could
possibly happen at any one time
e.g. a number could be both even and a multiple of three

9. Definitions
Probability
Probability:the chance of something happening
Sample Space:all possible outcomes
Equally Likely Events:events which have an equal chance of
happening
Mutually Exclusive Events:only one possible outcome can occur at
any one time.
e.g. a coin can be either a head or a tail, not both
Non-Mutually Exclusive Events:more than one outcome could
possibly happen at any one time
e.g. a number could be both even and a multiple of three
P E  : probability of E happening

10. Definitions
Probability
Probability:the chance of something happening
Sample Space:all possible outcomes
Equally Likely Events:events which have an equal chance of
happening
Mutually Exclusive Events:only one possible outcome can occur at
any one time.
e.g. a coin can be either a head or a tail, not both
Non-Mutually Exclusive Events:more than one outcome could
possibly happen at any one time
e.g. a number could be both even and a multiple of three
P E  : probability of E happening
P E  : probability of E not happening

11. Probability Theory

12. Probability Theory
0  P E   1

13. Probability Theory
0  P E   1
P(E)=0: E never happens

14. Probability Theory
0  P E   1
P(E)=0: E never happens
P(E)=1: a certain event. E must happen

15. Probability Theory
0  P E   1
P(E)=0: E never happens
P(E)=1: a certain event. E must happen
n E 
P E  
n S 

16. Probability Theory
0  P E   1
P(E)=0: E never happens
P(E)=1: a certain event. E must happen
n E  n E  : the number of times E occurs
P E  
n S 

17. Probability Theory
0  P E   1
P(E)=0: E never happens
P(E)=1: a certain event. E must happen
n E  n E  : the number of times E occurs
P E  
n S  nS  : total number of possibilities

18. Probability Theory
0  P E   1
P(E)=0: E never happens
P(E)=1: a certain event. E must happen
n E  n E  : the number of times E occurs
P E  
n S  nS  : total number of possibilities
e.g. A pair of dice are thrown. What is the probability that they;
(i) total 3?
(ii) total 7?

19. Probability Theory
0  P E   1
P(E)=0: E never happens
P(E)=1: a certain event. E must happen
n E  n E  : the number of times E occurs
P E  
n S  nS  : total number of possibilities
e.g. A pair of dice are thrown. What is the probability that they;
(i) total 3?
(ii) total 7?
1 1 2 1 3 1 4 1 5 1 6 1
1 2 2 2 3 2 4 2 5 2 6 2
1 3 2 3 3 3 4 3 5 3 6 3
1 4 2 4 3 4 4 4 5 4 6 4
1 5 2 5 3 5 4 5 5 5 6 5
1 6 2 6 3 6 4 6 5 6 6 6

20. Probability Theory
0  P E   1
P(E)=0: E never happens
P(E)=1: a certain event. E must happen
n E  n E  : the number of times E occurs
P E  
n S  nS  : total number of possibilities
e.g. A pair of dice are thrown. What is the probability that they;
(i) total 3?
(ii) total 7?
1 1 2 1 3 1 4 1 5 1 6 1
1 2 2 2 3 2 4 2 5 2 6 2
1 3 2 3 3 3 4 3 5 3 6 3
1 4 2 4 3 4 4 4 5 4 6 4
1 5 2 5 3 5 4 5 5 5 6 5
1 6 2 6 3 6 4 6 5 6 6 6

21. Probability Theory
0  P E   1
P(E)=0: E never happens
P(E)=1: a certain event. E must happen
n E  n E  : the number of times E occurs
P E  
n S  nS  : total number of possibilities
e.g. A pair of dice are thrown. What is the probability that they;
(i) total 3?
2
(ii) total 7? i P 3 
1 1 2 1 3 1 4 1 5 1 6 1 36
1 2 2 2 3 2 4 2 5 2 6 2
1 3 2 3 3 3 4 3 5 3 6 3
1 4 2 4 3 4 4 4 5 4 6 4
1 5 2 5 3 5 4 5 5 5 6 5
1 6 2 6 3 6 4 6 5 6 6 6

22. Probability Theory
0  P E   1
P(E)=0: E never happens
P(E)=1: a certain event. E must happen
n E  n E  : the number of times E occurs
P E  
n S  nS  : total number of possibilities
e.g. A pair of dice are thrown. What is the probability that they;
(i) total 3?
2
(ii) total 7? i P 3 
1 1 2 1 3 1 4 1 5 1 6 1 36
1 2 2 2 3 2 4 2 5 2 6 2 1
1 3 2 3 3 3 4 3 5 3 6 3

18
1 4 2 4 3 4 4 4 5 4 6 4
1 5 2 5 3 5 4 5 5 5 6 5
1 6 2 6 3 6 4 6 5 6 6 6

23. Probability Theory
0  P E   1
P(E)=0: E never happens
P(E)=1: a certain event. E must happen
n E  n E  : the number of times E occurs
P E  
n S  nS  : total number of possibilities
e.g. A pair of dice are thrown. What is the probability that they;
(i) total 3?
2
(ii) total 7? i P 3 
1 1 2 1 3 1 4 1 5 1 6 1 36
1 2 2 2 3 2 4 2 5 2 6 2 1
1 3 2 3 3 3 4 3 5 3 6 3

18
1 4 2 4 3 4 4 4 5 4 6 4
1 5 2 5 3 5 4 5 5 5 6 5
1 6 2 6 3 6 4 6 5 6 6 6

24. Probability Theory
0  P E   1
P(E)=0: E never happens
P(E)=1: a certain event. E must happen
n E  n E  : the number of times E occurs
P E  
n S  nS  : total number of possibilities
e.g. A pair of dice are thrown. What is the probability that they;
(i) total 3?
2 6
(ii) total 7? i P 3  ii P 7  
1 1 2 1 3 1 4 1 5 1 6 1 36 36
1 2 2 2 3 2 4 2 5 2 6 2 1
1 3 2 3 3 3 4 3 5 3 6 3

18
1 4 2 4 3 4 4 4 5 4 6 4
1 5 2 5 3 5 4 5 5 5 6 5
1 6 2 6 3 6 4 6 5 6 6 6

25. Probability Theory
0  P E   1
P(E)=0: E never happens
P(E)=1: a certain event. E must happen
n E  n E  : the number of times E occurs
P E  
n S  nS  : total number of possibilities
e.g. A pair of dice are thrown. What is the probability that they;
(i) total 3?
2 6
(ii) total 7? i P 3  ii P 7  
1 1 2 1 3 1 4 1 5 1 6 1 36 36
1 2 2 2 3 2 4 2 5 2 6 2 1 1
1 3 2 3 3 3 4 3 5 3 6 3
 
18 6
1 4 2 4 3 4 4 4 5 4 6 4
1 5 2 5 3 5 4 5 5 5 6 5
1 6 2 6 3 6 4 6 5 6 6 6

26. Complementary Events

27. Complementary Events
P E   1  P E 

28. Complementary Events
P E   1  P E 
e.g. What is the probability of totaling at least 3?

29. Complementary Events
P E   1  P E 
e.g. What is the probability of totaling at least 3?
P 3  1  P1 or 2 

30. Complementary Events
P E   1  P E 
e.g. What is the probability of totaling at least 3?
P 3  1  P1 or 2 
1
 1
36

31. Complementary Events
P E   1  P E 
e.g. What is the probability of totaling at least 3?
P 3  1  P1 or 2 
1
 1
36
35

36

32. Non-Mutually Exclusive Events

33. Non-Mutually Exclusive Events
P A  B   P A  P B   P AB 

34. Non-Mutually Exclusive Events
P A  B   P A  P B   P AB 
e.g. What is the chance of picking an Ace or a heart from a regular
deck of playing cards?

35. Non-Mutually Exclusive Events
P A  B   P A  P B   P AB 
e.g. What is the chance of picking an Ace or a heart from a regular
deck of playing cards?
PAce or heart   PAce  Pheart   PAce of hearts 

36. Non-Mutually Exclusive Events
P A  B   P A  P B   P AB 
e.g. What is the chance of picking an Ace or a heart from a regular
deck of playing cards?
PAce or heart   PAce  Pheart   PAce of hearts 
4 13 1
  
52 52 52

37. Non-Mutually Exclusive Events
P A  B   P A  P B   P AB 
e.g. What is the chance of picking an Ace or a heart from a regular
deck of playing cards?
PAce or heart   PAce  Pheart   PAce of hearts 
4 13 1
  
52 52 52
16

52
4

13

38. 2004 Mathematics HSC Q6c)
In a game, a turn involves rolling two dice, each with faces marked
0, 1, 2, 3, 4 and 5.
The score for each turn is calculated by multiplying the two
numbers uppermost on the dice.

39. 2004 Mathematics HSC Q6c)
In a game, a turn involves rolling two dice, each with faces marked
0, 1, 2, 3, 4 and 5.
The score for each turn is calculated by multiplying the two
numbers uppermost on the dice.
0X0=0 1X0=0 2X0=0 3X0=0 4X0=0 5X0=0
0X1=0 1X1=1 2X1=2 3X1=3 4X1=4 5X1=5
0X2=0 1X2=2 2X2=4 3X2=6 4X2=8 5 X 2 = 10
0X3=0 1X3=3 2X3=6 3X3=9 4 X 3 = 12 5 X 3 = 15
0X4=0 1X4=4 2X4=8 3 X 4 = 12 4 X 4 = 16 5 X 4 = 20
0X5=0 1X5=5 2 X 5 = 10 3 X 5 = 15 4 X 5 = 20 5 X 5 = 25

40. 2004 Mathematics HSC Q6c)
In a game, a turn involves rolling two dice, each with faces marked
0, 1, 2, 3, 4 and 5.
The score for each turn is calculated by multiplying the two
numbers uppermost on the dice.
0X0=0 1X0=0 2X0=0 3X0=0 4X0=0 5X0=0
0X1=0 1X1=1 2X1=2 3X1=3 4X1=4 5X1=5
0X2=0 1X2=2 2X2=4 3X2=6 4X2=8 5 X 2 = 10
0X3=0 1X3=3 2X3=6 3X3=9 4 X 3 = 12 5 X 3 = 15
0X4=0 1X4=4 2X4=8 3 X 4 = 12 4 X 4 = 16 5 X 4 = 20
0X5=0 1X5=5 2 X 5 = 10 3 X 5 = 15 4 X 5 = 20 5 X 5 = 25
(i) What is the probability
of scoring zero on the
first turn?

41. 2004 Mathematics HSC Q6c)
In a game, a turn involves rolling two dice, each with faces marked
0, 1, 2, 3, 4 and 5.
The score for each turn is calculated by multiplying the two
numbers uppermost on the dice.
0X0=0 1X0=0 2X0=0 3X0=0 4X0=0 5X0=0
0X1=0 1X1=1 2X1=2 3X1=3 4X1=4 5X1=5
0X2=0 1X2=2 2X2=4 3X2=6 4X2=8 5 X 2 = 10
0X3=0 1X3=3 2X3=6 3X3=9 4 X 3 = 12 5 X 3 = 15
0X4=0 1X4=4 2X4=8 3 X 4 = 12 4 X 4 = 16 5 X 4 = 20
0X5=0 1X5=5 2 X 5 = 10 3 X 5 = 15 4 X 5 = 20 5 X 5 = 25
(i) What is the probability
of scoring zero on the
first turn?

42. 2004 Mathematics HSC Q6c)
In a game, a turn involves rolling two dice, each with faces marked
0, 1, 2, 3, 4 and 5.
The score for each turn is calculated by multiplying the two
numbers uppermost on the dice.
0X0=0 1X0=0 2X0=0 3X0=0 4X0=0 5X0=0
0X1=0 1X1=1 2X1=2 3X1=3 4X1=4 5X1=5
0X2=0 1X2=2 2X2=4 3X2=6 4X2=8 5 X 2 = 10
0X3=0 1X3=3 2X3=6 3X3=9 4 X 3 = 12 5 X 3 = 15
0X4=0 1X4=4 2X4=8 3 X 4 = 12 4 X 4 = 16 5 X 4 = 20
0X5=0 1X5=5 2 X 5 = 10 3 X 5 = 15 4 X 5 = 20 5 X 5 = 25
(i) What is the probability
of scoring zero on the
first turn? 11
P  0  
36

43. 2004 Mathematics HSC Q6c)
In a game, a turn involves rolling two dice, each with faces marked
0, 1, 2, 3, 4 and 5.
The score for each turn is calculated by multiplying the two
numbers uppermost on the dice.
0X0=0 1X0=0 2X0=0 3X0=0 4X0=0 5X0=0
0X1=0 1X1=1 2X1=2 3X1=3 4X1=4 5X1=5
0X2=0 1X2=2 2X2=4 3X2=6 4X2=8 5 X 2 = 10
0X3=0 1X3=3 2X3=6 3X3=9 4 X 3 = 12 5 X 3 = 15
0X4=0 1X4=4 2X4=8 3 X 4 = 12 4 X 4 = 16 5 X 4 = 20
0X5=0 1X5=5 2 X 5 = 10 3 X 5 = 15 4 X 5 = 20 5 X 5 = 25
(i) What is the probability (ii) What is the probability of
of scoring zero on the scoring 16 or more on the
first turn? 11 first turn?
P  0  
36

44. 2004 Mathematics HSC Q6c)
In a game, a turn involves rolling two dice, each with faces marked
0, 1, 2, 3, 4 and 5.
The score for each turn is calculated by multiplying the two
numbers uppermost on the dice.
0X0=0 1X0=0 2X0=0 3X0=0 4X0=0 5X0=0
0X1=0 1X1=1 2X1=2 3X1=3 4X1=4 5X1=5
0X2=0 1X2=2 2X2=4 3X2=6 4X2=8 5 X 2 = 10
0X3=0 1X3=3 2X3=6 3X3=9 4 X 3 = 12 5 X 3 = 15
0X4=0 1X4=4 2X4=8 3 X 4 = 12 4 X 4 = 16 5 X 4 = 20
0X5=0 1X5=5 2 X 5 = 10 3 X 5 = 15 4 X 5 = 20 5 X 5 = 25
(i) What is the probability (ii) What is the probability of
of scoring zero on the scoring 16 or more on the
first turn? 11 first turn?
P  0  
36

45. 2004 Mathematics HSC Q6c)
In a game, a turn involves rolling two dice, each with faces marked
0, 1, 2, 3, 4 and 5.
The score for each turn is calculated by multiplying the two
numbers uppermost on the dice.
0X0=0 1X0=0 2X0=0 3X0=0 4X0=0 5X0=0
0X1=0 1X1=1 2X1=2 3X1=3 4X1=4 5X1=5
0X2=0 1X2=2 2X2=4 3X2=6 4X2=8 5 X 2 = 10
0X3=0 1X3=3 2X3=6 3X3=9 4 X 3 = 12 5 X 3 = 15
0X4=0 1X4=4 2X4=8 3 X 4 = 12 4 X 4 = 16 5 X 4 = 20
0X5=0 1X5=5 2 X 5 = 10 3 X 5 = 15 4 X 5 = 20 5 X 5 = 25
(i) What is the probability (ii) What is the probability of
of scoring zero on the scoring 16 or more on the
first turn? 11 first turn? 4
P  0   P 16  
36 36

46. 2004 Mathematics HSC Q6c)
In a game, a turn involves rolling two dice, each with faces marked
0, 1, 2, 3, 4 and 5.
The score for each turn is calculated by multiplying the two
numbers uppermost on the dice.
0X0=0 1X0=0 2X0=0 3X0=0 4X0=0 5X0=0
0X1=0 1X1=1 2X1=2 3X1=3 4X1=4 5X1=5
0X2=0 1X2=2 2X2=4 3X2=6 4X2=8 5 X 2 = 10
0X3=0 1X3=3 2X3=6 3X3=9 4 X 3 = 12 5 X 3 = 15
0X4=0 1X4=4 2X4=8 3 X 4 = 12 4 X 4 = 16 5 X 4 = 20
0X5=0 1X5=5 2 X 5 = 10 3 X 5 = 15 4 X 5 = 20 5 X 5 = 25
(i) What is the probability (ii) What is the probability of
of scoring zero on the scoring 16 or more on the
first turn? 11 first turn? 4
P  0   P 16  
36 36
1

9

47. (iii) What is the probability that the sum of the scores in the first
two turns is less than 45?

48. (iii) What is the probability that the sum of the scores in the first
two turns is less than 45?
P 45  1  P 45

49. (iii) What is the probability that the sum of the scores in the first
two turns is less than 45?
P 45  1  P 45
 1  P20,25  P25,20   P25,25

50. (iii) What is the probability that the sum of the scores in the first
two turns is less than 45?
P 45  1  P 45
 1  P20,25  P25,20   P25,25
2 1 1 2 1 1
 1     
36 36 36 36 36 36

51. (iii) What is the probability that the sum of the scores in the first
two turns is less than 45?
P 45  1  P 45
 1  P20,25  P25,20   P25,25
2 1 1 2 1 1 1291
 1      
36 36 36 36 36 36 1296

52. (iii) What is the probability that the sum of the scores in the first
two turns is less than 45?
P 45  1  P 45
 1  P20,25  P25,20   P25,25
2 1 1 2 1 1 1291
 1      
36 36 36 36 36 36 1296
Exercise 10A; odd
Exercise 10B; odd
Exercise 10C; odd (not 23)