Post on 14-Dec-2015
S4 General
18 Apr 202318 Apr 2023
Likelihood Number Line
Combined Probabilities
Relative Frequency
ProbabilityProbabilityw
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Mutually Excusive Events
Independent Events
S4 General
18 Apr 202318 Apr 2023
Starter QuestionsStarter Questions
1. Find the value of x if 2x- 3=17
2. Calculate (- 5)+12 - 15
3. Calculate x:
4. Change 790cm into m
5. I f I toss a coin in the air what is the chance of getting a head?
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75o
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S4 General
18 Apr 202318 Apr 2023
ProbabilityProbability
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. Understand the probability Understand the probability line. line.
1. To understand probability in terms of the number line and calculate simple probabilities.
2.2. Calculate simply Calculate simply probabilities.probabilities.
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S4 General
18 Apr 202318 Apr 2023
ProbabilityProbabilityLikelihood LineLikelihood Line
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10.50
CertainEvensImpossibleNot very
likelyVerylikely
Winning theLottery
School Holidays
Baby BornA Boy
Seeing a butterfly
In July
Go backin time
S4 General
18 Apr 202318 Apr 2023
ProbabilityProbabilityLikelihood LineLikelihood Line
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10.50
CertainEvensImpossibleNot very
likelyVerylikely
Everyone getting100 % in test
HomeworkEvery week
Toss a coinThat land
Heads
It willSnow in winter Going without
Food for a year.
S4 General
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ProbabilityProbability
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To work out a probability
P(A) = number of outcomes
Total number of possible outcomes
Probability is ALWAYS in the range 0 to 1
S4 General
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ProbabilityProbabilityNumber Likelihood Number Likelihood
LineLine
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10.50
CertainEvensImpossible
1 2 3 54 76 8
0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.9
Q. What is the chance of picking a number between 1 – 8 ?
Q. What is the chance of picking a number that is even ?
Q. What is the chance of picking the number 1 ?
88
= 1
48
= 0.5
18 = 0.125
P =
P(E) =
P(1) =
S4 General
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ProbabilityProbabilityLikelihood LineLikelihood Line
10.50
CertainEvensImpossibleNot very
likelyVerylikely
Q. What is the chance of picking a red card ?
Q. What is the chance of picking a diamond ?
Q. What is the chance of picking ace ?
52= 0.5
1352
= 0.25452
= 0.08
26
0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.9
P (Red) =
P (D) =
P (Ace) =
52 cards in a pack of cards
18 Apr 202318 Apr 2023
Now try Ex 1A & 1BCh10 (page 123)
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ProbabilityProbabilityS4 General
S4 General
18 Apr 202318 Apr 2023
Starter QuestionsStarter Questions
1. Find the value of x if 3x- 3=27
2. Calculate x:
3. What is the chance of picking a face card from a pack of cards.
4. 331% of 2403
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37o
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S4 General
18 Apr 202318 Apr 2023
ProbabilityProbability
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. Construct combination Construct combination tables and tree diagrams. tables and tree diagrams.
1. To understand combined probability by constructing tables or tree diagrams. 2.2. Calculate probabilities Calculate probabilities
from tables or tree from tables or tree diagrams.diagrams.
Combined Probabilities
S4 General
18 Apr 202318 Apr 2023
Calculate Probability :
1. Both green
ProbabilityProbabilityw
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Traffic Light 1 Traffic Light 2
Combined Probabilities
On route to school I pass two sets of traffic light. They work independently.
Complete the table of all possible combinations
Traffic Light 1
Traffic light 2
(r,R)
(g,R)
(a,R)
(r,A)
(g,A)
(a,A)
(r,G)
(g,G)
(a,G)
A GR
a
g
r 1=9
5=9
2=9
2. At least one green
3. One is amber one red
S4 General
18 Apr 202318 Apr 2023
Calculate Probability :
1. Both green
ProbabilityProbabilityw
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Traffic Light 1 Traffic Light 2
Combined Probabilities
Another way of representing the data !Tree Diagram
T L 1
(r,R)
(g,R)
(a,R)
(r,A)
(g,A)
(a,A)
(r,G)
(g,G)
(a,G)
A
G
R
a
g
r 1=9
5=9
2=9
2. At least one green
3. One is amber one red
A
G
R
A
G
R
T L2
T L2
T L2
S4 General
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ProbabilityProbabilityw
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Key Points
1. List all combinations (using a suitable table or tree diagram)
2. Interpret information to calculate probabilities.
Combined Probabilities
18 Apr 202318 Apr 2023
Now try Exercise 2Ch10 (page 124)
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ProbabilityProbabilityS4 General
Combined Probabilities
S4 General
18 Apr 202318 Apr 2023
Starter QuestionsStarter Questions
2 4 + 3 5
o
1. Find the value of x if 2x- 5=9
2. Calculate x :
3.
4. What the the probability of throwing a double six with a pair of dice.
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120o
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S4 General
18 Apr 202318 Apr 2023
ProbabilityProbability
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. Know the term relative Know the term relative frequency.frequency.
1. To understand the term relative frequency.
2.2. Calculate relative Calculate relative frequency from data frequency from data given.given.
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Relative Frequency
S4 General
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ProbabilityProbabilityw
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Relative Frequency : How often an event happens compared to the total numberof events.
DanielDaniel FrancesFrances
Number of headsNumber of heads 2424 5555
Number of tossesNumber of tosses 6060 100100
Example
Joe has a R.F. of heads = 24 2
= = 0.460 5
Relative Frequency
S4 General
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ProbabilityProbabilityw
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Relative Frequency : How often an event happens compared to the total numberof events.
DanielDaniel FrancesFrances
Number of headsNumber of heads 2424 5555
Number of tossesNumber of tosses 6060 100100
Example
Frances has a R.F. of heads = 55
= 0.55100
Relative Frequency
S4 General
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ProbabilityProbabilityw
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Frances has a R.F. of heads= 0.55
Joe has a R.F. of heads = 0.4
Whose relative frequency is closer to P(H) ?
P(H) = 0.5 France’s R.F. is closer to P(H)
Note : The larger the random sample, the closerthe relative frequency is to the probability of the event
Relative Frequency
18 Apr 202318 Apr 2023
Now try Exercise 3Ch10 (page 126)
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ProbabilityProbabilityS4 General
Relative Frequency
S4 General
18 Apr 202318 Apr 2023
Starter QuestionsStarter Questions
o
1. Find the value of x if 4x=48
2. Calculate x :
3. What is the probability of picking a number less than 4 from a pack of cards
4. Find the average of the numbers 15, 25, 20?
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55o
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47o
S4 General
18 Apr 202318 Apr 2023
ProbabilityProbability
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. Understand the term Understand the term mutually exclusive.mutually exclusive.
1. To understand that the term mutually exclusive. Understand that we simply add probabilities with this property.
2.2. Calculate probabilities for Calculate probabilities for events that have this events that have this property.property.
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Mutually Exclusive
S4 General
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ProbabilityProbabilityw
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P(A or B) = P(A) + P(B)
Mutually Exclusive
When two events are MUTUALLY EXCLUSIVE
Cannot happen at the same
time
we can simply add their individual probabilities
“or” means
add
S4 General
18 Apr 202318 Apr 2023
ProbabilityProbabilityw
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Example : There are 12 balls in a box.
Mutually Exclusive
Q. What is the probability of picking a green ball.
Q. What is the probability of picking a white ball.
Q. What is the probability of picking a green OR white ball.
P(G) =412
312
P(W) =
P(G or W) = P(G) + P(W)312
4 + =
12712
18 Apr 202318 Apr 2023
Now try Ex 4A & 4B
Ch10 (page 127)
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ProbabilityProbabilityS4 General
Mutually Exclusive
S4 General
18 Apr 202318 Apr 2023
Starter QuestionsStarter Questions
o
1. Find the value of x if 5x=90
2. Calculate x :
3. What is the probability of picking a red or black card from a pack of cards.
4. Find the average of the numbers 9, 21, 40?
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xo
270o
S4 General
18 Apr 202318 Apr 2023
ProbabilityProbability
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. Understand when two Understand when two events are independent.events are independent.
1. To understand that if two events are independent we can simply multiply probabilities.
2.2. Calculate probabilities for Calculate probabilities for events that are events that are independent.independent.
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Independent Events
S4 General
18 Apr 202318 Apr 2023
Calculate P(R) for spinner 1
ProbabilityProbabilityw
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Spinner 1 Spinner 2
Independent Events
Write down all the possible outcomes when the two spinners are spun together.
Spinner 1
Spinner 2
(Y,Y)
(R,Y)
(G,Y)
(Y,G)
(R,G)
(G,G)
(Y,R)
(R,R)
(G,R)
G RY
G
R
Y
1=3
Calculate (R) for spinner 2
1=3
Notice from table P (R,R)
1=9
P(R,R) = P(R) x P(R)
S4 General
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ProbabilityProbabilityw
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Key Points
For two independent events A and B we can multiply the individual probabilities
P(A and B) = P(A) x P(B)
1. List all combinations.2. Calculate individual probabilities.3. Multiply them together.
Independent Events “and” means
multiply
Independent Events
18 Apr 202318 Apr 2023
Now try Exercise 5Ch10 (page 129)
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ProbabilityProbabilityS4 General
Independent Events