notes: page 40. probability denoted by p(event) this method for calculating probabilities is only...

NOTES Page 40

Probability

bull Denoted by P(Event)

outcomes total

outcomes favorable)( EP

This method for calculating probabilities is only appropriate when the outcomes of the sample space are equally likely

Experimental Probability

bull The relative frequency at which a chance experiment occursndashFlip a fair coin 30 times amp get 17

heads

30

17

Law of Large Numbers

bull As the number of repetitions of a chance experiment increase the difference between the relative frequency of occurrence for an event and the true probability approaches zero

Basic Rules of ProbabilityRule 1 Legitimate Values

For any event E 0 lt P(E) lt 1

Rule 2 Sample spaceIf S is the sample space P(S) = 1

Rule 3 Complement

For any event E P(E) + P(not E) = 1

Independentbull Two events are independent if knowing that

one will occur (or has occurred) does not change the probability that the other occursndash A randomly selected student is female - What is

the probability she plays soccer for RHS

ndash A randomly selected student is female - What is the probability she plays football for RHs

Independent

Not independent

Rule 4 Multiplication

If two events A amp B are independent

General rule

P(B) P(A) B) ampP(A

A)|P(B P(A) B) ampP(A

)( BAP

Independent)( BAP

Yes

)()( BPAP

What does this mean

Ex 1) A certain brand of light bulbs are defective five percent of the time You randomly pick a package of two such bulbs off the shelf of a store What is the probability that both bulbs are defective

Can you assume they are independent

00250505D) amp P(D

)( BAP

Independent)( BAP

Yes No

)()( BPAP )()|( APABP

Ex 2) There are seven girls and eight boys in a math class The teacher selects two students at random to answer questions on the board What is the probability that both students are girls

Are these events independent

2146

157

G) amp P(G

Ex 6) Suppose I will pick two cards from a standard deck without replacement What is the probability that I select two spades

Are the cards independent NO

P(A amp B) = P(A) P(B|A)

Read ldquoprobability of B given that A occursrdquo

P(Spade amp Spade) = 14 1251 = 117

The probability of getting a spade given that a spade has already been drawn

Rule 5 AdditionIf two events E amp F are disjoint

P(E or F) = P(E) + P(F)

(General) If two events E amp F are not disjoint

P(E or F) = P(E) + P(F) ndash P(E amp F)

)( FEP What does this mean

)( FEP Mutually exclusive

)()( FPEP

Yes

Ex 3) A large auto center sells cars made by many different manufacturers Three of these are Honda Nissan and Toyota Suppose that P(H) = 25 P(N) = 18 P(T) = 14 What is the probability that the next car sold is a Honda Nissan or Toyota

Are these disjoint events

P(H or N or T) =

P(not (H or N or T) =

yes

25 + 18+ 14 = 57

1 - 57 = 43

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP

Ex 4) Musical styles other than rock and pop are becoming more popular A survey of college students finds that the probability they like country music is 40 The probability that they liked jazz is 30 and that they liked both is 10 What is the probability that they like country or jazz

P(C or J) = 4 + 3 -1 = 6

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP

Independent Yes )()( FPEP

Ex 5)

If P(A) = 045 P(B) = 035 and A amp B are independent find P(A or B)Is A amp B disjoint

If A amp B are disjoint are they independent

Disjoint events do not happen at the same time

So if A occurs can B occur

Disjoint events are dependent

NO independent events cannot be disjoint

P(A or B) = P(A) + P(B) ndash P(A amp B)

How can you find the

probability of A amp B

P(A or B) = 45 + 35 - 45(35) = 06425

If independent

multiply

H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6

If a coin is flipped amp a die rolled at the same time what is the probability that you will get a tail or a number less than 3

T1

T2

T3

T4

T5

T6 H1

H3

H2

H5

H4

H6

Coin is TAIL Roll is LESS THAN 3

P (heads or even) = P(tails) + P(less than 3) ndash P(tails amp less than 3)

= 12 + 13 ndash 16= 23

Flipping a coin and rolling a die are independent events

Independence also implies the events are NOT disjoint (hence the overlap)

Count T1 and T2 only once

Sample Space

Ex 7) A certain brand of light bulbs are defective five percent of the time You randomly pick a package of two such bulbs off the shelf of a store What is the probability that exactly one bulb is defective

P(exactly one) = P(D amp DC) or P(DC amp D)

= (05)(95) + (95)(05)

= 095

Ex 8) A certain brand of light bulbs are defective five percent of the time You randomly pick a package of two such bulbs off the shelf of a store What is the probability that at least one bulb is defective

P(at least one) = P(D amp DC) or P(DC amp D) or (D amp D)

= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one

The probability that at least one outcome happens is 1 minus the probability that no outcomes happen

P(at least 1) = 1 ndash P(none)

Ex 8 revisited) A certain brand of light bulbs are defective five percent of the time You randomly pick a package of two such bulbs off the shelf of a store

What is the probability that at least one bulb is defective

P(at least one) = 1 - P(DC amp DC)

0975

Ex 9) For a sales promotion the manufacturer places winning symbols under the caps of 10 of all Dr Pepper bottles You buy a six-pack What is the probability that you win something

P(at least one winning symbol) =

1 ndash P(no winning symbols) 1 - 96 = 4686

Rule 7 Conditional Probability

bull A probability that takes into account a given condition

P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B

Ex 10) In a recent study it was found that the probability that a randomly selected student is a girl is 51 and is a girl and plays sports is 10 If the student is female what is the probability that she plays sports

196151

1

P(F)

F)P(S F)|P(S

Ex 11) The probability that a randomly selected student plays sports if they are male is 31 What is the probability that the student is male and plays sports if the probability that they are male is 49

1519

4931

P(M)

M)P(SM)|P(S

x

x

Probabilities from two way tables

Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359

12) What is the probability that the driver is a student

359195

)( StudentP



13) What is the probability that the driver drives a European car

35945

)( EuropeanP



14) What is the probability that the driver drives an American or Asian car

Disjoint359102212

)(

AsianorAmericanP



15) What is the probability that the driver is staff or drives an Asian car

Disjoint35947102164

)(

AsianorStaffP



16) What is the probability that the driver is staff and drives an Asian car

35947

)( AsianandStaffP



17) If the driver is a student what is the probability that they drive an American car

Condition195107

)|( StudentAmericanP



18) What is the probability that the driver is a student if the driver drives a European car

Condition 4533

)|( EuropeanStudentP

Example 19Management has determined that customers return 12 of the items assembled by inexperienced employees whereas only 3 of the items assembled by experienced employees are returned Due to turnover and absenteeism at an assembly plant inexperienced employees assemble 20 of the items Construct a tree diagram or a chart for this data

What is the probability that an item is returned

If an item is returned what is the probability that an inexperienced employee assembled it

P(returned) = 48100 = 0048

P(inexperienced|returned) = 2448 = 05

Returned Not returned

Total

Experienced 24 776 80

Inexperienced 24 176 20

Total 48 952 100

Homework

bullRead p 45 Explanation

bullComplete p 49

PowerPoint Presentation

Probability



Basic Rules of Probability

Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Probability

bull Denoted by P(Event)

outcomes total

outcomes favorable)( EP

This method for calculating probabilities is only appropriate when the outcomes of the sample space are equally likely



heads

30

17






Rule 3 Complement






Independent

Not independent



General rule

P(B) P(A) B) ampP(A


)( BAP

Independent)( BAP

Yes

)()( BPAP

What does this mean



00250505D) amp P(D

)( BAP

Independent)( BAP

Yes No




2146

157

G) amp P(G








P(E or F) = P(E) + P(F)





)()( FPEP

Yes



P(H or N or T) =


yes

25 + 18+ 14 = 57

1 - 57 = 43

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


P(C or J) = 4 + 3 -1 = 6

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


Ex 5)










P(A or B) = 45 + 35 - 45(35) = 06425

If independent

multiply

H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6


T1

T2

T3

T4

T5

T6 H1

H3

H2

H5

H4

H6



= 12 + 13 ndash 16= 23




Sample Space



= (05)(95) + (95)(05)

= 095



= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one






0975






P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38



heads

30

17






Rule 3 Complement






Independent

Not independent



General rule

P(B) P(A) B) ampP(A


)( BAP

Independent)( BAP

Yes

)()( BPAP

What does this mean



00250505D) amp P(D

)( BAP

Independent)( BAP

Yes No




2146

157

G) amp P(G








P(E or F) = P(E) + P(F)





)()( FPEP

Yes



P(H or N or T) =


yes

25 + 18+ 14 = 57

1 - 57 = 43

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


P(C or J) = 4 + 3 -1 = 6

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


Ex 5)










P(A or B) = 45 + 35 - 45(35) = 06425

If independent

multiply

H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6


T1

T2

T3

T4

T5

T6 H1

H3

H2

H5

H4

H6



= 12 + 13 ndash 16= 23




Sample Space



= (05)(95) + (95)(05)

= 095



= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one






0975






P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38






Rule 3 Complement






Independent

Not independent



General rule

P(B) P(A) B) ampP(A


)( BAP

Independent)( BAP

Yes

)()( BPAP

What does this mean



00250505D) amp P(D

)( BAP

Independent)( BAP

Yes No




2146

157

G) amp P(G








P(E or F) = P(E) + P(F)





)()( FPEP

Yes



P(H or N or T) =


yes

25 + 18+ 14 = 57

1 - 57 = 43

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


P(C or J) = 4 + 3 -1 = 6

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


Ex 5)










P(A or B) = 45 + 35 - 45(35) = 06425

If independent

multiply

H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6


T1

T2

T3

T4

T5

T6 H1

H3

H2

H5

H4

H6



= 12 + 13 ndash 16= 23




Sample Space



= (05)(95) + (95)(05)

= 095



= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one






0975






P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38





Independent

Not independent



General rule

P(B) P(A) B) ampP(A


)( BAP

Independent)( BAP

Yes

)()( BPAP

What does this mean



00250505D) amp P(D

)( BAP

Independent)( BAP

Yes No




2146

157

G) amp P(G








P(E or F) = P(E) + P(F)





)()( FPEP

Yes



P(H or N or T) =


yes

25 + 18+ 14 = 57

1 - 57 = 43

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


P(C or J) = 4 + 3 -1 = 6

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


Ex 5)










P(A or B) = 45 + 35 - 45(35) = 06425

If independent

multiply

H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6


T1

T2

T3

T4

T5

T6 H1

H3

H2

H5

H4

H6



= 12 + 13 ndash 16= 23




Sample Space



= (05)(95) + (95)(05)

= 095



= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one






0975






P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38



General rule

P(B) P(A) B) ampP(A


)( BAP

Independent)( BAP

Yes

)()( BPAP

What does this mean



00250505D) amp P(D

)( BAP

Independent)( BAP

Yes No




2146

157

G) amp P(G








P(E or F) = P(E) + P(F)





)()( FPEP

Yes



P(H or N or T) =


yes

25 + 18+ 14 = 57

1 - 57 = 43

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


P(C or J) = 4 + 3 -1 = 6

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


Ex 5)










P(A or B) = 45 + 35 - 45(35) = 06425

If independent

multiply

H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6


T1

T2

T3

T4

T5

T6 H1

H3

H2

H5

H4

H6



= 12 + 13 ndash 16= 23




Sample Space



= (05)(95) + (95)(05)

= 095



= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one






0975






P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

)( BAP

Independent)( BAP

Yes

)()( BPAP

What does this mean



00250505D) amp P(D

)( BAP

Independent)( BAP

Yes No




2146

157

G) amp P(G








P(E or F) = P(E) + P(F)





)()( FPEP

Yes



P(H or N or T) =


yes

25 + 18+ 14 = 57

1 - 57 = 43

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


P(C or J) = 4 + 3 -1 = 6

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


Ex 5)










P(A or B) = 45 + 35 - 45(35) = 06425

If independent

multiply

H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6


T1

T2

T3

T4

T5

T6 H1

H3

H2

H5

H4

H6



= 12 + 13 ndash 16= 23




Sample Space



= (05)(95) + (95)(05)

= 095



= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one






0975






P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38



00250505D) amp P(D

)( BAP

Independent)( BAP

Yes No




2146

157

G) amp P(G








P(E or F) = P(E) + P(F)





)()( FPEP

Yes



P(H or N or T) =


yes

25 + 18+ 14 = 57

1 - 57 = 43

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


P(C or J) = 4 + 3 -1 = 6

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


Ex 5)










P(A or B) = 45 + 35 - 45(35) = 06425

If independent

multiply

H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6


T1

T2

T3

T4

T5

T6 H1

H3

H2

H5

H4

H6



= 12 + 13 ndash 16= 23




Sample Space



= (05)(95) + (95)(05)

= 095



= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one






0975






P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

)( BAP

Independent)( BAP

Yes No




2146

157

G) amp P(G








P(E or F) = P(E) + P(F)





)()( FPEP

Yes



P(H or N or T) =


yes

25 + 18+ 14 = 57

1 - 57 = 43

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


P(C or J) = 4 + 3 -1 = 6

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


Ex 5)










P(A or B) = 45 + 35 - 45(35) = 06425

If independent

multiply

H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6


T1

T2

T3

T4

T5

T6 H1

H3

H2

H5

H4

H6



= 12 + 13 ndash 16= 23




Sample Space



= (05)(95) + (95)(05)

= 095



= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one






0975






P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38



2146

157

G) amp P(G








P(E or F) = P(E) + P(F)





)()( FPEP

Yes



P(H or N or T) =


yes

25 + 18+ 14 = 57

1 - 57 = 43

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


P(C or J) = 4 + 3 -1 = 6

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


Ex 5)










P(A or B) = 45 + 35 - 45(35) = 06425

If independent

multiply

H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6


T1

T2

T3

T4

T5

T6 H1

H3

H2

H5

H4

H6



= 12 + 13 ndash 16= 23




Sample Space



= (05)(95) + (95)(05)

= 095



= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one






0975






P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38








P(E or F) = P(E) + P(F)





)()( FPEP

Yes



P(H or N or T) =


yes

25 + 18+ 14 = 57

1 - 57 = 43

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


P(C or J) = 4 + 3 -1 = 6

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


Ex 5)










P(A or B) = 45 + 35 - 45(35) = 06425

If independent

multiply

H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6


T1

T2

T3

T4

T5

T6 H1

H3

H2

H5

H4

H6



= 12 + 13 ndash 16= 23




Sample Space



= (05)(95) + (95)(05)

= 095



= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one






0975






P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38



)()( FPEP

Yes



P(H or N or T) =


yes

25 + 18+ 14 = 57

1 - 57 = 43

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


P(C or J) = 4 + 3 -1 = 6

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


Ex 5)










P(A or B) = 45 + 35 - 45(35) = 06425

If independent

multiply

H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6


T1

T2

T3

T4

T5

T6 H1

H3

H2

H5

H4

H6



= 12 + 13 ndash 16= 23




Sample Space



= (05)(95) + (95)(05)

= 095



= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one






0975






P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38



P(H or N or T) =


yes

25 + 18+ 14 = 57

1 - 57 = 43

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


P(C or J) = 4 + 3 -1 = 6

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


Ex 5)










P(A or B) = 45 + 35 - 45(35) = 06425

If independent

multiply

H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6


T1

T2

T3

T4

T5

T6 H1

H3

H2

H5

H4

H6



= 12 + 13 ndash 16= 23




Sample Space



= (05)(95) + (95)(05)

= 095



= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one






0975






P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


P(C or J) = 4 + 3 -1 = 6

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


Ex 5)










P(A or B) = 45 + 35 - 45(35) = 06425

If independent

multiply

H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6


T1

T2

T3

T4

T5

T6 H1

H3

H2

H5

H4

H6



= 12 + 13 ndash 16= 23




Sample Space



= (05)(95) + (95)(05)

= 095



= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one






0975






P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38


P(C or J) = 4 + 3 -1 = 6

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


Ex 5)










P(A or B) = 45 + 35 - 45(35) = 06425

If independent

multiply

H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6


T1

T2

T3

T4

T5

T6 H1

H3

H2

H5

H4

H6



= 12 + 13 ndash 16= 23




Sample Space



= (05)(95) + (95)(05)

= 095



= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one






0975






P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

)( FEP


)()( FPEP

Yes No

)()()( FEPFPEP


Ex 5)










P(A or B) = 45 + 35 - 45(35) = 06425

If independent

multiply

H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6


T1

T2

T3

T4

T5

T6 H1

H3

H2

H5

H4

H6



= 12 + 13 ndash 16= 23




Sample Space



= (05)(95) + (95)(05)

= 095



= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one






0975






P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Ex 5)










P(A or B) = 45 + 35 - 45(35) = 06425

If independent

multiply

H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6


T1

T2

T3

T4

T5

T6 H1

H3

H2

H5

H4

H6



= 12 + 13 ndash 16= 23




Sample Space



= (05)(95) + (95)(05)

= 095



= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one






0975






P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6


T1

T2

T3

T4

T5

T6 H1

H3

H2

H5

H4

H6



= 12 + 13 ndash 16= 23




Sample Space



= (05)(95) + (95)(05)

= 095



= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one






0975






P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38



= (05)(95) + (95)(05)

= 095



= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one






0975






P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38



= (05)(95) + (95)(05) + (05)(05)

= 0975

Rule 6 At least one






0975






P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Rule 6 At least one






0975






P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38




0975






P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38






P(A)

B)P(AA)|P(B

P(given)

P(and)A)|P(B


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38


196151

1

P(F)

F)P(S F)|P(S


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38


1519

4931

P(M)

M)P(SM)|P(S

x

x




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38




359195

)( StudentP




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38




35945

)( EuropeanP




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38




Disjoint359102212

)(

AsianorAmericanP




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38




Disjoint35947102164

)(

AsianorStaffP




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38




35947

)( AsianandStaffP




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38




Condition195107





Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38




Condition 4533





P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38




P(returned) = 48100 = 0048



Total



Total 48 952 100

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Homework


bullComplete p 49


Probability




Slide 6

Independent

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26


Slide 28

Slide 29


Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

notes: page 40. probability denoted by p(event) this method for calculating probabilities is only...

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