S4 General 12-Apr-15 Likelihood Number Line Combined Probabilities Relative Frequency Probability ...

S4 General

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Likelihood Number Line

Combined Probabilities

Relative Frequency

ProbabilityProbabilityw

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Mutually Excusive Events

Independent Events

S4 General

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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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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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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

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10.50


likelyVerylikely

Everyone getting100 % in test

HomeworkEvery week

Toss a coinThat land

Heads

It willSnow in winter Going without

Food for a year.

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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

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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) =

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10.50


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

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Now try Ex 1A & 1BCh10 (page 123)

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ProbabilityProbabilityS4 General

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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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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.


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Calculate Probability :

1. Both green


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Traffic Light 1 Traffic Light 2


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

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Calculate Probability :

1. Both green


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Traffic Light 1 Traffic Light 2


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

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Key Points

1. List all combinations (using a suitable table or tree diagram)

2. Interpret information to calculate probabilities.


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Now try Exercise 2Ch10 (page 124)

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2 4 + 3 5

o


2. Calculate x :

3.

4. What the the probability of throwing a double six with a pair of dice.

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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

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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

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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

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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

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Relative Frequency

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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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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

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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

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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

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Now try Ex 4A & 4B

Ch10 (page 127)

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Mutually Exclusive

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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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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

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Calculate P(R) for spinner 1


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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)

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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

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Independent Events

S4 General 12-Apr-15 Likelihood Number Line Combined Probabilities Relative Frequency Probability ...

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