12x1 t09 01 definitions and theory (2010)
TRANSCRIPT
ProbabilityDefinitions
ProbabilityDefinitionsProbability:the chance of something happening
ProbabilityDefinitionsProbability:the chance of something happeningSample Space:all possible outcomes
ProbabilityDefinitionsProbability:the chance of something happeningSample Space:all possible outcomes
Equally Likely Events:events which have an equal chance of happening
ProbabilityDefinitionsProbability:the chance of something happeningSample 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 happeningSample 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 happeningSample 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 happeningSample 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 happeningSample Space:all possible outcomes
Equally Likely Events:events which have an equal chance of happening
happeningofy 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 happeningSample Space:all possible outcomes
Equally Likely Events:events which have an equal chance of happening
happeningofy 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
SnEnEP
P(E)=1: a certain event. E must happen
Probability Theory 10 EP
P(E)=0: E never happens
SnEnEP
P(E)=1: a certain event. E must happen
occursEtimesofnumber the:En
Probability Theory 10 EP
P(E)=0: E never happens
SnEnEP
P(E)=1: a certain event. E must happen
occursEtimesofnumber the:En iespossibilitofnumber total:Sn
Probability Theory 10 EP
P(E)=0: E never happens
SnEnEP
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?
occursEtimesofnumber the:En iespossibilitofnumber total:Sn
Probability Theory 10 EP
P(E)=0: E never happens
SnEnEP
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 41 51 6
2 12 22 32 42 52 6
3 13 23 33 43 53 6
4 14 24 34 44 54 6
5 15 25 35 45 55 6
6 16 26 36 46 56 6
occursEtimesofnumber the:En iespossibilitofnumber total:Sn
Probability Theory 10 EP
P(E)=0: E never happens
SnEnEP
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 41 51 6
2 12 22 32 42 52 6
3 13 23 33 43 53 6
4 14 24 34 44 54 6
5 15 25 35 45 55 6
6 16 26 36 46 56 6
occursEtimesofnumber the:En iespossibilitofnumber total:Sn
Probability Theory 10 EP
P(E)=0: E never happens
SnEnEP
3623 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?
occursEtimesofnumber the:En iespossibilitofnumber total:Sn
1 11 21 31 41 51 6
2 12 22 32 42 52 6
3 13 23 33 43 53 6
4 14 24 34 44 54 6
5 15 25 35 45 55 6
6 16 26 36 46 56 6
Probability Theory 10 EP
P(E)=0: E never happens
SnEnEP
3623 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
occursEtimesofnumber the:En iespossibilitofnumber total:Sn
1 11 21 31 41 51 6
2 12 22 32 42 52 6
3 13 23 33 43 53 6
4 14 24 34 44 54 6
5 15 25 35 45 55 6
6 16 26 36 46 56 6
Probability Theory 10 EP
P(E)=0: E never happens
SnEnEP
3623 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 41 51 6
2 12 22 32 42 52 6
3 13 23 33 43 53 6
4 14 24 34 44 54 6
5 15 25 35 45 55 6
6 16 26 36 46 56 6
181
occursEtimesofnumber the:En iespossibilitofnumber total:Sn
Probability Theory 10 EP
P(E)=0: E never happens
SnEnEP
3623 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 41 51 6
2 12 22 32 42 52 6
3 13 23 33 43 53 6
4 14 24 34 44 54 6
5 15 25 35 45 55 6
6 16 26 36 46 56 6
181
3667 Pii
occursEtimesofnumber the:En iespossibilitofnumber total:Sn
Probability Theory 10 EP
P(E)=0: E never happens
SnEnEP
3623 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 41 51 6
2 12 22 32 42 52 6
3 13 23 33 43 53 6
4 14 24 34 44 54 6
5 15 25 35 45 55 6
6 16 26 36 46 56 6
181
3667 Pii
61
occursEtimesofnumber the:En iespossibilitofnumber 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
3611
Complementary Events
EPEP 1
e.g. What is the probability of totaling at least 3? 2or 113 PP
3611
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?
heartsofAceheartAceheartor 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?
heartsofAceheartAceheartor 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?
heartsofAceheartAceheartor 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?
36110 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?
36110 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?
36110 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?
36110 P
(ii) What is the probability of scoring 16 or more on the first turn?
36416 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?
36110 P
(ii) What is the probability of scoring 16 or more on the first turn?
36416 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
3621
(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
3621 1296
1291
(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
3621 1296
1291
Exercise 10A; odd
Exercise 10B; odd
Exercise 10C; odd (not 23)