12x1 t09 01 definitions & theory
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ProbabilityDefinitions
ProbabilityDefinitionsProbability:the chance of something happening
ProbabilityDefinitionsProbability:the chance of something happening
Sample Space:all possible outcomes
ProbabilityDefinitionsProbability:the chance of something happening
Sample Space:all possible outcomes
Equally Likely Events:events which have an equal chance of happening
ProbabilityDefinitionsProbability: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.
ProbabilityDefinitionsProbability: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
ProbabilityDefinitionsProbability: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 bothNon-Mutually Exclusive Events:more than one outcome could
possibly happen at any one time
ProbabilityDefinitionsProbability: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 bothNon-Mutually Exclusive Events:more than one outcome could
possibly happen at any one timee.g. a number could be both even and a multiple of three
ProbabilityDefinitionsProbability:the chance of something happening
Sample Space:all possible outcomes
Equally Likely Events:events which have an equal chance of happening
happening ofy probabilit : EEP
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 bothNon-Mutually Exclusive Events:more than one outcome could
possibly happen at any one timee.g. a number could be both even and a multiple of three
ProbabilityDefinitionsProbability:the chance of something happening
Sample Space:all possible outcomes
Equally Likely Events:events which have an equal chance of happening
happening ofy probabilit : EEP
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 bothNon-Mutually Exclusive Events:more than one outcome could
possibly happen at any one timee.g. a number could be both even and a multiple of three
happeningnot ofy probabilit : EEP
Probability Theory
Probability Theory 10 EP
Probability Theory 10 EP
P(E)=0: E never happens
Probability Theory 10 EP
P(E)=0: E never happens
P(E)=1: a certain event. E must happen
Probability Theory 10 EP
P(E)=0: E never happens
SnEn
EP
P(E)=1: a certain event. E must happen
Probability Theory 10 EP
P(E)=0: E never happens
SnEn
EP
P(E)=1: a certain event. E must happen
occurs E timesofnumber the:En
Probability Theory 10 EP
P(E)=0: E never happens
SnEn
EP
P(E)=1: a certain event. E must happen
occurs E timesofnumber the:En
iespossibilit ofnumber total:Sn
Probability Theory 10 EP
P(E)=0: E never happens
SnEn
EP
P(E)=1: a certain event. E must happen
e.g. A pair of dice are thrown. What is the probability that they;(i) total 3?(ii) total 7?
occurs E timesofnumber the:En
iespossibilit ofnumber total:Sn
Probability Theory 10 EP
P(E)=0: E never happens
SnEn
EP
P(E)=1: a certain event. E must happen
e.g. A pair of dice are thrown. What is the probability that they;(i) total 3?(ii) total 7?
1 11 21 31 4
1 51 6
2 1
2 22 32 42 52 6
3 13 23 33 43 53 6
4 14 24 34 44 54 6
5 15 25 3
5 45 55 6
6 16 26 36 46 56 6
occurs E timesofnumber the:En
iespossibilit ofnumber total:Sn
Probability Theory 10 EP
P(E)=0: E never happens
SnEn
EP
P(E)=1: a certain event. E must happen
e.g. A pair of dice are thrown. What is the probability that they;(i) total 3?(ii) total 7?
1 11 21 31 4
1 51 6
2 1
2 22 32 42 52 6
3 13 23 33 43 53 6
4 14 24 34 44 54 6
5 15 25 3
5 45 55 6
6 16 26 36 46 56 6
occurs E timesofnumber the:En
iespossibilit ofnumber total:Sn
Probability Theory 10 EP
P(E)=0: E never happens
SnEn
EP
362
3 Pi
P(E)=1: a certain event. E must happen
e.g. A pair of dice are thrown. What is the probability that they;(i) total 3?(ii) total 7?
occurs E timesofnumber the:En
iespossibilit ofnumber total:Sn
1 11 21 31 4
1 51 6
2 1
2 22 32 42 52 6
3 13 23 33 43 53 6
4 14 24 34 44 54 6
5 15 25 3
5 45 55 6
6 16 26 36 46 56 6
Probability Theory 10 EP
P(E)=0: E never happens
SnEn
EP
362
3 Pi
P(E)=1: a certain event. E must happen
e.g. A pair of dice are thrown. What is the probability that they;(i) total 3?(ii) total 7?
181
occurs E timesofnumber the:En
iespossibilit ofnumber total:Sn
1 11 21 31 4
1 51 6
2 1
2 22 32 42 52 6
3 13 23 33 43 53 6
4 14 24 34 44 54 6
5 15 25 3
5 45 55 6
6 16 26 36 46 56 6
Probability Theory 10 EP
P(E)=0: E never happens
SnEn
EP
362
3 Pi
P(E)=1: a certain event. E must happen
e.g. A pair of dice are thrown. What is the probability that they;(i) total 3?(ii) total 7?
1 11 21 31 4
1 51 6
2 1
2 22 32 42 52 6
3 13 23 33 43 53 6
4 14 24 34 44 54 6
5 15 25 3
5 45 55 6
6 16 26 36 46 56 6
181
occurs E timesofnumber the:En
iespossibilit ofnumber total:Sn
Probability Theory 10 EP
P(E)=0: E never happens
SnEn
EP
362
3 Pi
P(E)=1: a certain event. E must happen
e.g. A pair of dice are thrown. What is the probability that they;(i) total 3?(ii) total 7?
1 11 21 31 4
1 51 6
2 1
2 22 32 42 52 6
3 13 23 33 43 53 6
4 14 24 34 44 54 6
5 15 25 3
5 45 55 6
6 16 26 36 46 56 6
181
366
7 Pii
occurs E timesofnumber the:En
iespossibilit ofnumber total:Sn
Probability Theory 10 EP
P(E)=0: E never happens
SnEn
EP
362
3 Pi
P(E)=1: a certain event. E must happen
e.g. A pair of dice are thrown. What is the probability that they;(i) total 3?(ii) total 7?
1 11 21 31 4
1 51 6
2 1
2 22 32 42 52 6
3 13 23 33 43 53 6
4 14 24 34 44 54 6
5 15 25 3
5 45 55 6
6 16 26 36 46 56 6
181
366
7 Pii
61
occurs E timesofnumber the:En
iespossibilit ofnumber total:Sn
Complementary Events
Complementary Events
EPEP 1
Complementary Events
EPEP 1
e.g. What is the probability of totaling at least 3?
Complementary Events
EPEP 1
e.g. What is the probability of totaling at least 3?
2or 113 PP
Complementary Events
EPEP 1
e.g. What is the probability of totaling at least 3?
2or 113 PP
361
1
Complementary Events
EPEP 1
e.g. What is the probability of totaling at least 3?
2or 113 PP
361
1
3635
Non-Mutually Exclusive Events
Non-Mutually Exclusive Events
ABPBPAPBAP
Non-Mutually Exclusive Events
ABPBPAPBAP
e.g. What is the chance of picking an Ace or a heart from a regular deck of playing cards?
Non-Mutually Exclusive Events
ABPBPAPBAP
e.g. What is the chance of picking an Ace or a heart from a regular deck of playing cards?
hearts of AceheartAceheartor Ace PPPP
Non-Mutually Exclusive Events
ABPBPAPBAP
e.g. What is the chance of picking an Ace or a heart from a regular deck of playing cards?
hearts of AceheartAceheartor Ace PPPP
521
5213
524
Non-Mutually Exclusive Events
ABPBPAPBAP
e.g. What is the chance of picking an Ace or a heart from a regular deck of playing cards?
hearts of AceheartAceheartor Ace PPPP
521
5213
524
1345216
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.
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.
2004 Mathematics HSC Q6c)
0 X 0 = 00 X 1 = 00 X 2 = 00 X 3 = 00 X 4 = 00 X 5 = 0
1 X 0 = 01 X 1 = 11 X 2 = 21 X 3 = 31 X 4 = 41 X 5 = 5
2 X 0 = 02 X 1 = 22 X 2 = 42 X 3 = 62 X 4 = 82 X 5 = 10
3 X 0 = 03 X 1 = 33 X 2 = 63 X 3 = 93 X 4 = 123 X 5 = 15
4 X 0 = 04 X 1 = 44 X 2 = 84 X 3 = 124 X 4 = 164 X 5 = 20
5 X 0 = 05 X 1 = 55 X 2 = 105 X 3 = 155 X 4 = 205 X 5 = 25
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.
2004 Mathematics HSC Q6c)
(i) What is the probability of scoring zero on the first turn?
0 X 0 = 00 X 1 = 00 X 2 = 00 X 3 = 00 X 4 = 00 X 5 = 0
1 X 0 = 01 X 1 = 11 X 2 = 21 X 3 = 31 X 4 = 41 X 5 = 5
2 X 0 = 02 X 1 = 22 X 2 = 42 X 3 = 62 X 4 = 82 X 5 = 10
3 X 0 = 03 X 1 = 33 X 2 = 63 X 3 = 93 X 4 = 123 X 5 = 15
4 X 0 = 04 X 1 = 44 X 2 = 84 X 3 = 124 X 4 = 164 X 5 = 20
5 X 0 = 05 X 1 = 55 X 2 = 105 X 3 = 155 X 4 = 205 X 5 = 25
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.
2004 Mathematics HSC Q6c)
0 X 0 = 00 X 1 = 00 X 2 = 00 X 3 = 00 X 4 = 00 X 5 = 0
1 X 0 = 01 X 1 = 11 X 2 = 21 X 3 = 31 X 4 = 41 X 5 = 5
2 X 0 = 02 X 1 = 22 X 2 = 42 X 3 = 62 X 4 = 82 X 5 = 10
3 X 0 = 03 X 1 = 33 X 2 = 63 X 3 = 93 X 4 = 123 X 5 = 15
4 X 0 = 04 X 1 = 44 X 2 = 84 X 3 = 124 X 4 = 164 X 5 = 20
5 X 0 = 05 X 1 = 55 X 2 = 105 X 3 = 155 X 4 = 205 X 5 = 25
(i) What is the probability of scoring zero on the first turn?
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.
2004 Mathematics HSC Q6c)
0 X 0 = 00 X 1 = 00 X 2 = 00 X 3 = 00 X 4 = 00 X 5 = 0
1 X 0 = 01 X 1 = 11 X 2 = 21 X 3 = 31 X 4 = 41 X 5 = 5
2 X 0 = 02 X 1 = 22 X 2 = 42 X 3 = 62 X 4 = 82 X 5 = 10
3 X 0 = 03 X 1 = 33 X 2 = 63 X 3 = 93 X 4 = 123 X 5 = 15
4 X 0 = 04 X 1 = 44 X 2 = 84 X 3 = 124 X 4 = 164 X 5 = 20
5 X 0 = 05 X 1 = 55 X 2 = 105 X 3 = 155 X 4 = 205 X 5 = 25
(i) What is the probability of scoring zero on the first turn?
3611
0 P
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.
2004 Mathematics HSC Q6c)
0 X 0 = 00 X 1 = 00 X 2 = 00 X 3 = 00 X 4 = 00 X 5 = 0
1 X 0 = 01 X 1 = 11 X 2 = 21 X 3 = 31 X 4 = 41 X 5 = 5
2 X 0 = 02 X 1 = 22 X 2 = 42 X 3 = 62 X 4 = 82 X 5 = 10
3 X 0 = 03 X 1 = 33 X 2 = 63 X 3 = 93 X 4 = 123 X 5 = 15
4 X 0 = 04 X 1 = 44 X 2 = 84 X 3 = 124 X 4 = 164 X 5 = 20
5 X 0 = 05 X 1 = 55 X 2 = 105 X 3 = 155 X 4 = 205 X 5 = 25
(i) What is the probability of scoring zero on the first turn?
3611
0 P
(ii) What is the probability of scoring 16 or more on the first turn?
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.
2004 Mathematics HSC Q6c)
0 X 0 = 00 X 1 = 00 X 2 = 00 X 3 = 00 X 4 = 00 X 5 = 0
1 X 0 = 01 X 1 = 11 X 2 = 21 X 3 = 31 X 4 = 41 X 5 = 5
2 X 0 = 02 X 1 = 22 X 2 = 42 X 3 = 62 X 4 = 82 X 5 = 10
3 X 0 = 03 X 1 = 33 X 2 = 63 X 3 = 93 X 4 = 123 X 5 = 15
4 X 0 = 04 X 1 = 44 X 2 = 84 X 3 = 124 X 4 = 164 X 5 = 20
5 X 0 = 05 X 1 = 55 X 2 = 105 X 3 = 155 X 4 = 205 X 5 = 25
(i) What is the probability of scoring zero on the first turn?
3611
0 P
(ii) What is the probability of scoring 16 or more on the first turn?
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.
2004 Mathematics HSC Q6c)
0 X 0 = 00 X 1 = 00 X 2 = 00 X 3 = 00 X 4 = 00 X 5 = 0
1 X 0 = 01 X 1 = 11 X 2 = 21 X 3 = 31 X 4 = 41 X 5 = 5
2 X 0 = 02 X 1 = 22 X 2 = 42 X 3 = 62 X 4 = 82 X 5 = 10
3 X 0 = 03 X 1 = 33 X 2 = 63 X 3 = 93 X 4 = 123 X 5 = 15
4 X 0 = 04 X 1 = 44 X 2 = 84 X 3 = 124 X 4 = 164 X 5 = 20
5 X 0 = 05 X 1 = 55 X 2 = 105 X 3 = 155 X 4 = 205 X 5 = 25
(i) What is the probability of scoring zero on the first turn?
3611
0 P
(ii) What is the probability of scoring 16 or more on the first turn?
364
16 P
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.
2004 Mathematics HSC Q6c)
0 X 0 = 00 X 1 = 00 X 2 = 00 X 3 = 00 X 4 = 00 X 5 = 0
1 X 0 = 01 X 1 = 11 X 2 = 21 X 3 = 31 X 4 = 41 X 5 = 5
2 X 0 = 02 X 1 = 22 X 2 = 42 X 3 = 62 X 4 = 82 X 5 = 10
3 X 0 = 03 X 1 = 33 X 2 = 63 X 3 = 93 X 4 = 123 X 5 = 15
4 X 0 = 04 X 1 = 44 X 2 = 84 X 3 = 124 X 4 = 164 X 5 = 20
5 X 0 = 05 X 1 = 55 X 2 = 105 X 3 = 155 X 4 = 205 X 5 = 25
(i) What is the probability of scoring zero on the first turn?
3611
0 P
(ii) What is the probability of scoring 16 or more on the first turn?
364
16 P
91
(iii) What is the probability that the sum of the scores in the first two turns is less than 45?
(iii) What is the probability that the sum of the scores in the first two turns is less than 45?
45145 PP
(iii) What is the probability that the sum of the scores in the first two turns is less than 45?
45145 PP 25,2520,2525,201 PPP
(iii) What is the probability that the sum of the scores in the first two turns is less than 45?
45145 PP 25,2520,2525,201 PPP
361
361
362
361
361
362
1
(iii) What is the probability that the sum of the scores in the first two turns is less than 45?
45145 PP 25,2520,2525,201 PPP
361
361
362
361
361
362
1 12961291
(iii) What is the probability that the sum of the scores in the first two turns is less than 45?
45145 PP 25,2520,2525,201 PPP
361
361
362
361
361
362
1 12961291
Exercise 10A; odd
Exercise 10B; odd
Exercise 10C; odd (not 23)