3 probability[1] (1).ppt

8/9/2019 3 Probability[1] (1).ppt

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1

Weather forecas

Psychology

GamesSports

Chapter

3

Elementary Statistics

Larson Farber

Probability

Business

Medicine


2/25

LarsonFarber Ch! 3

"

{1 2 3 4 5 6}

{Die is even}={2 4 6}

{4}

Roll a dieProbability experiment:

#n action through $hich counts%measurements or responses are obtained

Sample spae:

&he set of all possible outcomes

!vent:

# subset of the sample space!

"#tome:

&he result of a single trial

$mportant %erms


3/25

LarsonFarber Ch! 3

3

Probability !xperiment:#n action through $hich counts%measurements% or responses are obtained

Sample Spae:&he set of all possible

outcomes

!vent:# subset of the sample space!

"#tome:&he result of a single trial

&'oose a ar (rom prod#tion line

)not'er !xperiment


4/25

LarsonFarber Ch! 3

'

&lassial(e)ually probable outcomes*

spacsampleinoutcomesof+umber

,e-entinoutcomesof+umberP(,* =

Fre)uency&otal

,e-entofFre)uencyP(,* =

Probability blood pressure $ill decrease

after medication

Probability the line $ill be busy

!mpirial

$nt#ition

%ypes o( Probability


5/25

LarsonFarber Ch! 3

.

&$o dice are rolled!

/escribe the

sample space!

1stroll

30outcomes

"nd

roll

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%ree Dia*rams


6/25

LarsonFarber Ch! 3

0

1%1

1%"

1%3

1%'

1%.

1%0

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"%"

"%3

"%'

"%.

"%0

3%1

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Find the probability the sum is '

Find the probability the sum is 11

Find the probability the sum is ' or 11

Sample Spaces and Probabilities

&$o dice are rolled and the sum is noted!


7/25

LarsonFarber Ch! 3

&omplementary !vents

&heomplement of e-ent , is e-ent ,!,consists of all the e-ents in the sample space

that are notin e-ent ,!

%'e day+s prod#tion onsists o( 12

ars, 5 o( -'i' are de(etive. $( one ar is

seleted at random, (ind t'e probability it

is not de(etive.

! !

Sol#tion:

P/de(etive0 = 512

P/not de(etive0 = 1 512 = 12 = .53

P(,2* 1 4 P(,*


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5

%'e probability an event -ill o#r, *iven /on

t'e ondition0 t'at anot'er event ) 'as o#rred.

&$o cars are selected from a production line of

1" cars $here . are defecti-e! What is the

probability the "nd car is defecti-e%giventhe first

car $as defecti-e6

We $rite this as P(B7#* and say 8probability

of B% gi-en #9!

Gi-en a defecti-e car has been selected% the

conditional sample space: ' defecti-e out of 11!

So% P(B7#* '11

&onditional Probability


9/25

;

&$o dice are rolled% find the probability

the second die is a '% gi-en the first $as a '


10/25

1?

&$o e-ents # and B are independent if

the probability of the occurrence of

e-ent B is not affected by the occurrence

(or non4occurrence* of e-ent #!

)= ta7in* an aspirin ea' day

= 'avin* a 'eart atta7

)= bein* a (emale

= bein* #nder 648 tall

&$o e-ents that are not independent are

dependent.

)= ein* (emale

=9avin* type " blood

)= irst 'ild is a boy

= Seond 'ild is a bo

$ndependent !vents


11/25


12/25

1"

&he follo$ing is the result of a mar@et research poll! # sample

of adults $as as@ed if they li@ed a ne$ Auice!

1! P(es*

"! P(Seattle*

3! P(Miami*

'! P(+o% gi-en Miami*

.! P(+ot Seattle*

0! P(Seattle% gi-en yes*

! P(es% gi-en Seattle*

5! P(Miami% gi-en


13/25

13

1! P(es*

"! P(Seattle*

3! P(Miami*

'! P(+o% gi-en Miami*

1?? 1.? 1.?

1". 13? ;. 3.?

. 1? . ".?


14/25

1'

1?? 1.? 1.?

1". 13? ;. 3.?

. 1? . ".?


15/25

1.

#re e-ents # Seattle and B es independent e-ents6

#re e-ents # Miami and B


16/25

10

&o find the probability that t$o e-ents% # and B$ill occur in se)uence% multiply the probability

# occurs by the conditional probability B

occurs% gi-en # has occurred!

P( # and B* P(#* E P(B7#*

&$o cars are selected from a production line of 1"

$here . are defecti-e! Find the probability both cars

re defecti-e!

# first car is defecti-e B second car is defecti-e

P(#* .1" P(B7#* '11

P(# and B* .1" E '11 .33 ?!1"1


17/25

LarsonFarber Ch! 3

1

&$o dice are rolled! Find the probability both are 's!

# first die is a ' and B second die is a '!

P(#* 10 P(B7#* 10

P(# and B* 10 E 10 130 ?!?"5

When t$o e-ents # and B are

independent% then

P (# and B* P(#* E P(B*

+ote for independent e-ents P(B* and P(B7#* are the same!

Multiplication ule


18/25

15


19/25

1;

on


20/25


21/25

"1

&ontin*eny %able&he follo$ing is the result of a mar@et

research poll for sample of adults $ereas@ed if they li@ed a ne$ Auice!

'! P(Miami or es*

.! P(


22/25

""

&ontin*eny %able

1! P(Miami and es*

"! P(


23/25


24/25

LarsonFarber Ch! 3

"'

Summary

Probability at least oneof t$o e-ents occur

P(# or B* P(#* K P(B* 4 P(# and B*#dd the t$o simple probabilities but dont

orget to subtract the probability of both

ccurring! &his pre-ents double counting!

For complementary e-entsP(,* 1 4 P(,*

Subtract the probability of the e-ent from one

&he probabilitybothof t$o e-ents occur

P(# and B* P(#* P(B7#*Multiply the probability of the first e-ent

times the conditional probability the seconde-ent occurs% gi-en the first occurred!


25/25

#ndamental &o#ntin* Priniple

f one e-ent can occur m$ays and a second e-ent canccur n$ays% the number of $ays the t$o e-ents can

ccur in se)uence is mn. This rule can be extended

or any number of events occurring in a sequence.

Df a meal consists of " choices of soup% 3 main dishes

and " desserts% ho$ many different meals can be selected6

5

1" meals

1

"

.

0

;

1?

11

1"

3

'

Start

"

Soup

3

Main

"

/essert

3 probability[1] (1).ppt

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