1 m

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Probability: What are the C

hances?

Question

Topic

Answ

er1

Idea of probability C

2 Idea of random

ness A

3 Idea of probability/M

yths D

4 Idea of probability/M

yths B

5 Idea of probability/M

yths A

6 Idea of probability/M

yths C

7 Idea of random

ness D

8 Probability M

yths D

9 Probability M

yths B

10 Sim

ulation to estimate probability

D] 1

Simulation to estim

ate probability D

12 Sim

ulation to estimate probability

E13

Simulation to estim

ate probability E

14 Sim

ulation to estimate probability

E15

Sim

ulation to estimate probability

B16

Sample space

D17

Sample space

B18

Sample space

B19

Sample space

C20

Sample space

B21

Basic Probability R

ules D

22 A

ddition of disjoint events A

23 M

ultiplication Rule, Independent events

C24

Basic Probability R

ules C

25 C

omplem

ent rule D

26 A

ddition of disjoint events C

27 B

asic Probability Rules

E28

Addition of disjoint events

B29

Mutually exclusive events

B30

Multiplication R

ule, Independent events E

31 C

omplem

ent rule E

32 M

utually exclusive events A

33 M

utually exclusive events C

34 Independent and m

utually exclusive events D

35 Independent and m

utually exclusive events C

36 G

eneral addition rule C

37 G

eneral addition rule (and multiplication of indep. events)

D38

Multiplication R

ule, Independent events; Com

plement

B39

Multiplication R

ule, Independent events A

40 M

ultiplication Rule, Independent events; C

omplem

ent C

41 Independent and m

utually exclusive events C

42 M

ultiplication Rule, Independent events

C43

General addition rule (and m

ultiplication of indep. events) D

44 Intersection of events

A45

Union of events

C46

Multiplication R

ule, Independent events E

47 C

onditional probability formula

B48

Conditional probability form

ula D

AT

£

O

The Practice of Statistics for A

P*, 4th edition

85

49 C

onditional probability formula

50 V

enn diagrams

51 V

enn diagrams

52 M

ultiplication rule, dependent events

53 C

onditional probability formula

54 Probabilities from

tree diagram55

Probabilities from tree diagram

56 Probabilities from

tree diagram57

Probabilities from tree diagram

58 C

onditional probability from 2-w

ay table59

Conditional probability from

2-way table

60 T

ree diagram from

probabilities

61 V

enn diagrams

62 V

enn diagrams

63 C

onditional probability from 2-w

ay table64

Conditional probability from

2-way table

65 C

onditional probability from 2-w

ay table66

Venn diagram

s67

Venn diagram

s68

Venn diagram

s69

Conditional probability from

2-way table

70 C

onditional probability from 2-w

ay table71

Conditional probability from

2-way table

ACADEACDDAEADDDDEEDBEDC

86C

hapter 5: Probability: What are the C

hances?

1.1

toss

a p

enny

and

obs

erve

whe

ther

it l

ands

hea

ds u

p or

tail

s up

. Sup

pose

the

penn

y is

fai

r, i.

e., t

hepr

obab

ility

of

head

s is

1/2

and

the

prob

abil

ity o

f ta

ils

is 1

/2. T

his

mea

ns th

atoc

curr

ence

of

a he

ad m

ust b

e ba

lanc

ed b

y a

tail

in o

ne o

f the

nex

t tw

o or

thre

e to

sses

.if

I fl

ip th

e co

in 1

0 ti

mes

, it w

ould

be

alm

ost

impo

ssib

le to

obt

ain

7 he

ads

and

3 ta

ils.

flip

the

coi

n m

any,

man

y ti

mes

the

prop

orti

on o

f he

ads

wil

l be

app

roxi

mat

ely

1/2,

and

this

"pro

port

ion

wil

l ten

d to

get

clo

ser

and

clos

er to

1/2

as

the

num

ber o

f to

sses

inc

reas

es.

"E

rega

rdle

ss o

f the

num

ber

of f

lips

, hal

f wil

l be

hea

ds a

nd h

alf t

ails

.jE

j)fa

ll of

the

abov

e.A

NS:

C

TO

P: I

dea

of p

roba

bilit

y

2. I

f th

e in

divi

dual

out

com

es o

f a

phen

omen

on a

re u

ncer

tain

, but

ther

e is

non

ethe

less

a re

gula

rdi

stri

butio

n of

out

com

es i

n a

larg

e nu

mbe

r of

repe

titio

ns,

we

say

the

phen

omen

on i

s/A

jtan

dom

.B

) pr

edic

tabl

e.C

) uni

form

.D

) pr

obab

le.

E) n

orm

al.

AN

S: A

T

OP:

Ide

a of

ran

dom

ness

3. W

hen

two

coin

s ar

e to

ssed

, the

pro

babi

lity

of

getti

ng tw

o he

ads

is 0

.25.

Thi

s m

eans

that

A)

of e

very

100

toss

es, e

x^t

ly 2

5 w

ill h

ave

two

head

s.B

) th

e c^

cts

agai

nst t

wo

head

s ar

e 4

to 1

.

fn th

e lo

ng ru

n, th

e av

erag

e nu

mbe

r of

head

s is

0.2

5.in

the

long

run

two

head

s w

ill o

ccur

on

25%

of

all t

osse

s.

,f

you

get t

wo

head

s on

eac

h of

the

firs

t fiv

e to

sses

of

the

coin

s, y

ou a

re u

njjk

^ly

to g

et h

eads

the

four

th t

ime.

AN

S: D

T

OP:

Ide

a of

pro

babi

lity/

Myt

hs

4. If

I to

ss a

fair

coi

n 50

00 t

imes

find

I ge

t any

thin

g ot

her

than

250

0 he

ads,

then

som

ethi

ng is

wro

ng w

ith th

e w

ay I

flip

coi

ns,

he p

ropo

rtio

n of

hea

ds w

ill b

e cl

ose

to 0

.5i r

un o

f 10

hea

ds i

n a

row

wil

l inc

j^as

e th

e pr

obab

ilit

y of

get

ting

a r

un o

f 10

tai

ls in

a r

ow.

D)

the

prop

ortio

n of

hea

ds i

n th

ese

toss

es is

a p

aram

eter

E) 0

e p

ropo

rtio

n of

hea

ds w

ill b

e cl

ose

to 5

0.A

NS:

B

TO

P: I

dea

of p

roba

bilit

y/M

yths

5. Y

ou r

ead

in a

boo

k on

pok

er t

hat t

he p

roba

bili

ty o

f be

ing

deal

t thr

ee o

f a

kind

in a

fiv

e-ca

rd p

oker

han

dis

1/5

0. W

hat

does

thi

s m

ean?

(A) I

f yo

u de

al t

hous

ands

of

poke

r ha

nds,

the

fra

ctio

n of

them

that

con

tain

thre

e of

a k

ind

wil

l be

very

ctos

e to

1/5

0.B

) If

you

dea

l 50

poke

r ha

nds,

then

one

of

them

wil

l con

tain

thre

e of

a k

ind.

C)

If y

ou d

eal

10,0

00 p

oker

han

ds, t

hen

200

of th

em w

ill

cont

ain

thre

e of

a k

ind.

D)

A p

roba

bilit

y of

0.0

2 is

som

ebod

y's

best

gue

ss f

or a

pro

babi

lity

of

bein

g de

alt t

hree

of

a ki

nd.

E)

It d

oesn

't m

ean

anyt

hing

, bec

ause

1/5

0 is

just

a n

umbe

r.A

NS

: A

TO

P:

Idea

of p

roba

bilit

y/M

yths

The

Prac

tice

of S

tatis

tics

for A

P*, 4

lh e

ditio

n 87

6. A

bas

ketb

all p

laye

r m

akes

160

out

of

200

free

thr

ows.

We

wou

ld es

timat

e th

e pr

obab

ility

that

the

play

er m

akes

his

nex

t fr

ee th

row

to b

eA

) 0.1

6.; e

ithe

r he

mak

es i

t or h

e do

esn'

t. 1

/ ,

/ ^

p'*"

/,y<j

f'i ~~

*' c3

E)8

0.A

NS

:CT

OP:

Ide

a of

pro

babi

lity/

Myt

hs

up.

. In

prob

abil

ity

and

stat

istic

s, a

ran

dom

phe

nom

enon

is

-A)

som

ethi

ng th

at is

com

pjgl

ely-

unex

pect

ed o

r sur

pris

ing

B)

som

ethi

ng-t

hat h

as a

lim

ited

set o

f ou

tcom

es, b

ut w

hen

each

out

com

e oc

curs

is

com

plet

ely

unpr

edic

tabl

e.C

) so

met

hing

that

app

ears

unp

redi

ctab

le, b

ut e

ach

indi

vidu

al o

utco

me

caa-

btt a

ocuf

atel

ypre

Hic

ted

with

appr

opri

ate

mat

hem

atic

al o

r co

mpu

ter

mod

elin

g.(1

5 so

met

hing

that

is

unpr

edic

tabl

e fro

m o

ne o

ccur

renc

e to

the

next

, but

ove

r th

e co

urse

of m

any

occu

rren

ces

follo

ws

a pr

edic

tabl

e pa

ttern

E)

som

ethi

ng w

hose

out

com

e ds

fjes-

jdes

erip

tion.

AN

S: D

T

OP

: Ide

a of

ran

dom

ness

18. Y

ou a

re p

layi

ng a

boa

rd g

ame

with

som

e fr

iend

s th

at in

volv

es r

ollin

g tw

o si

x-si

ded

dice

. Fo

r ei

ght

cons

ecut

ive

rolls

, the

sum

on

the

dice

isj

S. W

hich

of t

he f

ollo

win

g st

atem

ents

is tr

ue?

A)

Eac

h ti

me

you

roll

ano

ther

6, t

he p

roba

bili

ty o

f ge

ttin

g ye

t ano

ther

6 o

n th

e ne

xt r

oll;

B)

Eac

h ti

me

you

roll

ano

ther

6, t

he p

roba

bili

ty o

f get

ting

yet a

noth

er 6

on

the

next

rol

l sh

ould

fin

d an

oth^

^ejt

of d

ice:

eig

ht c

onse

cutiv

e 6's

is im

poss

ible

with

fai

r dic

e,pr

obab

ility

of

rolli

ng a

6 o

n th

e ni

nth

roll

is th

e sa

me

as it

was

on

the

firs

t rol

l,to

ne o

f th

ese

stat

emen

ts i

s tru

e.A

NS:

D

TO

P:

Pro

babi

lity

Myt

hs

^p9. A

pok

er p

laye

r is

dea

lt po

or h

ands

for

seve

ral

hour

s. H

e de

cide

s to

bet

hea

vily

on

the

last

han

d of

the

even

ing

on th

e gr

ound

s th

at a

fter

man

y ba

d ha

nds

he i

s du

e fo

r a

win

ner.

A)

He'

s I'H

jKt,

beca

use

the

win

ning

s ha

ve to

ave

rage

out.

(SnH

e's

wro

ng,

beca

use

succ

essi

ve d

eals

are

inde

pend

ent o

f ea

ch o

ther

,cj

He's

Yjg

frt,

beca

use

succ

essi

ve d

eals

are

inde

pend

ent o

f ea

ch o

ther

.D

) He'

s wro

ng, b

ecau

se h

e's

clea

rly

on a

"cd

Wst

reak

."E

) W

heth

er h

e's

righ

t or

wro

ng d

epen

ds o

n now

^iny

bad

han

ds h

e's

been

dea

lt so

far

.A

NS:

B

TO

P:

Pro

babi

lity

Myt

hs

(£lO

. You

wan

t to

use

sim

ulat

ion

to e

stim

ate

the

prob

abili

ty o

f ge

tting

exa

ctly

one

hea

d an

d on

e ta

il in

two

toss

esjo

f a

fair

coi

n.,Y

ou a

ssig

n th

e di

gits

0, 1

, 2, 3

,4 to

hea

ds a

nd 5

, 6, 7

, 8, 9

to ta

ils. U

sing

the

follo

win

g ra

ndom

dig

its t

o ex

ecut

e as

man

y si

mul

atio

ns_a

sj>o

ssib

le, w

hat i

s yo

ur e

stim

ate

of th

epr

obab

ility

? (I

Tta

*

T^W

\

A)

1/20

B) 1

/10

C)

5/10

E)2

/3A

NS

:D

o-4

=

e.xp

<

TO

P: S

imul

atio

n to

est

imat

e pr

obab

ilit

y

fP»

11. A

box

has

\10

ticke

ts )i

n it

,[tw

pofw

hich

are

win

ning

tic

ket

! Y

ou d

raw

a ti

cket

at r

ando

m. I

f it

's a

win

ning

tick

et, y

ou w

in. I

f not

Tyo

lTge

t ano

ther

cha

nce,

as

follo

ws:

you

r lo

siin

gjic

ket

is r

epla

cejl

jrrt

he.

bo

x by

_a w

jnni

ng t

icke

t (so

now

ther

e ar

e 10

tick

ets,

as

befo

re, b

ut 3

of t

hem

are

win

ning

tick

ets)

. You

get t

o dr

aw a

gain

, at r

ando

m. W

hich

of

the

foll

owin

g ar

e le

giti

mat

e m

etho

ds fo

r usi

ng s

imul

atio

n to

e|ti

mat

e th

e pr

obab

ility

of w

inni

ng?

___J

L^

i^*1

^ ~

^CJC

Cho

ose,

at r

ando

m, a

two-

digi

t nu

mbe

r. I

f the

fir

st d

igit

is^O

or 1

j you

win

on

the

firs

t dr

aw; I

f the

fir

stdi

git

is 2

thro

ugh

9, b

ut th

e se

cond

dig

it is

0,

1, o

r 2,

you

win

on

the

seco

nd d

raw

. A

ny o

ther

two-

digi

tnu

mbe

r mea

ns y

ou l

ose.

Th

e/-v

4 w

•

^"M

"" ~r

~t c'c

e'r

5

vJfT

Cho

ose,

at r

ando

m, a

one

-dig

it nu

mbe

r. I

f it

is-O

prL

you

win

. If

it is

2 th

roug

h 9,

pic

k a

seco

ndnu

mbe

r. I

f the

sec

ond

num

ber i

s 8,

9,_o

rO. y

ou w

irT

TO

ther

wis

e, y

ou lo

se.

£ ^

E/J-

TS, ^°

>T

III.

Cho

ose,

at r

ando

m, a

one

^cfig

it nu

mbe

r. I

f it

is 0

or

1, y

ou w

in o

n th

e fi

rst

draw

. If

itj^

2,

3, o

f 4,

n>

you

win

on

the

seco

nd d

raw

; If

it is

5 th

roug

h 9,

you

lose

. "

A)

I on

lyB

) II

onl

y' o

nly

: and

II

E)

I, I

I, a

nd I

IIA

NS:

D

TO

P:

Sim

ulat

ion

to e

stim

ate

prob

abili

ty

f»

12. A

bas

ketb

all

play

er m

akes

2/3

of

his

free

thro

ws.

To

sim

ulat

e a

sing

le fr

ee th

row

, w

hich

of

the

foll

owin

g as

sign

men

ts o

f di

gits

to m

akin

g a

free

thr

ow a

re a

ppro

pria

te?

vl. 0

and

1 c

orre

spon

d to

mak

ing

the

free

thr

ow a

nd 2

cor

resp

onds

to

mis

sing

the

free

thro

w,

^l 2

)V

II. 0

1,02

, 03,

04,

05,

06,

07,

and

08

corr

espo

nd t

o m

akin

g th

e fr

ee th

row

and

09,

10,

11,

and

12

y/Z

. "

corr

espo

nd to

mis

sing

the

free

thr

ow.

via

. Use

a d

ie a

nd le

t 1,

2,3

, and

4 c

orre

spon

d to

mak

ing

a fr

ee th

row

whi

le 5

and

6 c

orre

spon

d to

mis

sing

LJ

a fr

ee t

hrow

.A

) I o

nly

"

B)

II o

nly

C)

III o

nly

D) I

and

III

(E)X

II,

and

III

AN

S: E

T

OP

: Sim

ulat

ion

to e

stim

ate

prob

abili

ty ^

5 \£

~

- S

HO

TS

13. A

bas

ketb

all

play

er m

akes

l 75%

of h

is f

ree

thro

ws.

We

wan

t to

estim

ate

the

prob

abil

ity

that

he

mak

es4

or m

ore

free

s th

row

s ou

t of

S^tte

TnpT

slJw

e as

sum

Fth

e sh

ots

are

inde

pend

ent)

. T

o do

this

, we

use

the

digi

ts 1

, 2, a

nd 3

to c

orre

spon

d to

mak

ing

the

free

thro

w a

nd th

e di

git 4

to c

orre

spon

d to

mis

sing

the

free

thro

w. I

f the

tab

le o

f ra

ndom

dig

its

begi

ns w

ith th

e di

gits

bel

ow,

how

man

y fr

ee t

hrow

doe

s he

hit

in o

urfi

rst

sim

ulat

ion

of f

ive

shot

s?

B)2

C)3

5830

1

AN

S: E

,

TO

P:

Sim

ulat

ion

to e

stim

ate

p

I /2

.Z

- 3

^

^

"? \

Y \

<$

e c

The

Pra

ctic

e of

Sta

tistic

s fo

r A

P*,

4*

editi

on

89

Use

the

follo

win

g to

ans

wer

que

stio

ns 1

4 —

15:

Scen

ario

5-1

' /

"2.

To

sim

ulat

e a

toss

of a

coi

n w

e le

t the

dig

its 0

, 1, 2

, 3, a

nd 4

cor

resp

ondj

ojji

ead

and

the

digi

ts 5

, 6, 7

, j,

fio 9

cor

re^r

jond

JcLa

JajJ

. C

onsi

der

the

follo

win

g ga

me:

We"

are

goin

g to

loss

lhe

coin

unt

il w

e ei

ther

geT

aTie

ad o

fwe

get t

wo

tails

in a

row

, whi

chev

er c

omes

firs

t. If

it ta

kes u

s on

e to

ss to

get

the

head

we

win

$2, i

f it t

akes

us

two

toss

es w

e w

in $

1, a

nd if

we

get t

wo

tail

s in

a ro

w w

e w

in n

othi

ng. U

se th

e fo

llow

ing

sequ

ence

of r

ando

m d

igits

to s

imul

ate

this

gam

e as

man

y ti

mes

as p

ossi

ble:

f)

^212

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w

$s

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cena

rio

5-1.

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ed o

n yo

ur s

imul

ajjo

rj, t

he e

stim

ated

pro

tA

) 1/

4.

TO

P: S

imul

atio

n to

est

imat

e pr

obab

ility

15. S

cena

rio

5-1.

Bas

ed o

n yo

ur si

mul

atio

n, th

e es

timat

ed p

roba

bilit

y of

win

ning

not

hing

isA

IL/2

^

Q2

/15

.D

)6/1

5.E

) 7/1

1.A

NS:

B

TO

P: S

imul

atio

n to

estim

ate

prob

abil

ity

16. T

he c

olle

ctio

n of

all

poss

ible

out

com

es o

f ar

ando

m p

heno

men

on is

cal

led

A) a

cen

sus.

B) t

he p

roba

bilit

y.C

) a c

hanc

e exp

erim

ent

(D))

he s

ampl

e spa

ce.

E) t

he d

istr

ibut

ion.

AN

S: D

T

OP:

Sam

ple

spac

e

B L

*cic

, £ e

D

17.1

(sel

ect t

wo

card

s fr

om a

dec

k of

52

card

s an

d ob

serv

e th

e co

lor

of e

ach

(26

card

s in

the

deck

are

red

and

26 a

reT>

Iack

)TW

hich

of t

he f

ollo

win

g is

an

appr

opri

ate

sam

ple

spac

e S

for t

he p

ossi

ble

outc

omes

?=

{re

d, b

lack

}=

{(r

ed, r

ed),

(red

, bla

ck),

(bla

ck, r

ed),

(bla

ck, b

lack

)}, w

here

, for

exa

mpl

e, (r

ed, r

ed)

stan

ds f

orth

e ev

ent "

the

first

car

d is

red

and

the

seco

nd c

ard

is re

d."

C) S

= {

(red

, red

), (r

ed, b

lack

), (b

lack

, bla

ck)}

, whe

re, f

or e

xam

ple,

(red

, red

) st

ands

for

the

even

t"t

he fi

rst c

ard

is re

d an

d th

e se

cond

car

d jV

fVd.

" <

:'

M L

5 s

D) 5

= {

0,1,

2}.

E) A

ll of

the

abov

e.A

NS:

B

TO

P: S

ampl

e sp

ace

£ ft

90C

hapt

er 5

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babi

lity

: W

hat a

re th

e C

hanc

es?

18. A

bas

ketb

all p

laye

r sh

oots

8 f

ree

thro

ws

duri

ng a

gam

e. T

he s

ampl

e sp

ace

for

coun

ting

the

num

ber

she m

akes

is

-^

~~

betw

een

0 an

d 1.

,/

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+-,

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KH

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3

o I

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0 t

oSi =

who

le n

umbe

rs^K

to 8

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S

ill s

eque

nces

of

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ts o

r mis

ses,

lik

e H

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ple

spac

e

19. A

gam

e co

nsis

ts o

f dr

awin

g th

ree

card

s at

ran

dom

fro

m a

dec

k of

pla

ying

car

ds.

You

win

$3

for

each

red

card

tha

t is

dra

wn.

It c

osts

$2~

to^I

ayT

For

^)ne

^lay

ofth

is g

ame,

the

sam

ple

spac

e S

for t

he n

etam

ount

you

win

(aft

er d

educ

ting

the

cost

of p

lay)

is

°

Qe.

d =

o -

z

~ -|

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={

$0

,$1

,$2

,$3

} /

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d

- 3

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-.

jCI^

={-^

lL..$4.$

7b

D) 5

= {

-$2, $

3, $

6, $

9}E

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{$

0,$

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6,$

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S: C

T

OP:

Sam

ple

spac

e

20. S

uppo

se th

ere

are

thre

e ca

rds

in a

dec

k, o

ne m

arke

d w

ith a

1, o

ne m

arke

d w

ith a

2, a

nd o

ne m

arke

dw

ith a

5. Y

ou d

raw

two

card

s at

ran

dom

and

wit

hout

repl

acem

ent f

rom

the

dec

k of

thre

e ca

rds.

The

sam

ple

spac

e 5

= {

(1, 2

), (

1, 5

), (

2, 5

)} c

onsi

sts

of th

ese

thre

e eq

uall

y li

kely

out

com

es.

Let

Xbe

the

sum

of th

e nu

mbe

rs o

n th

e tw

o ca

rds

draw

n. W

hich

of

the

foll

owin

g is

the

corr

ect s

et o

f pr

obab

ilitie

s fo

r^Y

?

B)

AN

S:B

C)

TO

P: S

ampl

e sp

ace

D)

E)

21. A

n as

sign

men

t of p

roba

bilit

ies

mus

t ob

ey w

hich

of t

he f

ollo

win

g?v A

) T

he p

roba

bilit

y of

any

eve

nt m

ust b

e a

num

ber b

etw

een

0 an

d 1,

incl

usiv

e./B

) T

he s

um o

f al

l the

pro

babi

liti

es o

f al

l ou

lcon

^sT

nlri

e sa

mpl

e sp

ace

ii/C

) T

he p

roba

bilit

y of

an

even

t is

the

sum

of t

he p

roba

bilit

ies

of o

utc

om

esn

hea

mp

le s

pace

inw

hich

the

even

t oc

curs

.JD

))A11

thre

e of

the

abov

e.E

) A

and

B o

nly.

AN

S: D

T

OP:

Bas

ic P

roba

bilit

y R

ules

22. E

vent

A h

as p

roba

bili

ty 0

.4.

Eve

nt B

has

pro

babi

lity

0.5

. If

A a

nd B

are

dis

join

t, th

en th

e pr

obab

ility

that

bot

h ev

ents

occ

ur i

s

C)

0.2.

D)

0.7.

E)

0.9.

AN

S: A

TO

P:

Ad

dit

ion

of d

isjo

int

even

ts

The

Pra

ctic

e of

Sta

tistic

s fo

r A

P*,

4th

edi

tion

91

23. E

vent

A h

as p

roba

bilit

y 0.4

. Eve

nt B

has

pro

babi

lity

0.5.

If A

and

B a

re in

depe

nden

t, th

en th

epr

obab

ility

that

bot

h ev

ents

occ

ur is

A) 0

.0.

JIO

J^Q

O^

D) 0

.7.

E) 0

.9.

AN

S:C

TO

P: M

ulti

plic

atio

n R

ule,

Ind

epen

dent

eve

nts

Use

the

foll

owin

g to

ans

wer

que

stio

ns 2

4 -

26

:

Scen

ario

5-2

If y

ou d

raw

an

M&

M c

andy

at r

ando

m f

rom

a b

ag o

f the

can

dies

, th

e ca

ndy

you

draw

will

hav

e on

e of

six

colo

rs. T

he p

roba

bilit

y of

dra

win

g ea

ch c

olor

dep

ends

on

the

prop

ortio

n of

eac

h co

lor

amon

g al

l can

dies

mad

e. T

he ta

ble

belo

w g

ives

the

prob

abili

ty th

at a

rand

omly

cho

sen

M&

M h

ad e

ach

colo

r be

fore

blu

e M

& M

's re

plac

ed ta

n in

199

5.

Col

orPr

obab

ilit

yB

row

n0.

3R

ed 0.2

Yel

low

31G

reen

0.1

Ora

nge

0.1

Tan

0.1

24. U

se S

cena

rio 5

-2. T

he p

roba

bilit

y of

dra

win

g a

yello

w c

andy

isA

)0.

BJ.

l.C

))2.

T

Vie

-^o

^-)

E)

impo

ssib

le to

det

erm

ine f

rom

the

info

rmat

ion

give

n.A

NS:

C

TO

P:

Bas

ic P

roba

bilit

y R

ules

25. U

se S

cena

rio 5

-2. T

he p

roba

bilit

y th

at y

ou d

o no

t dra

w a

red

cand

y is

A)

.2.

B).

3. f7. 8. mpo

ssib

le to

det

erm

ine

from

the

inf

orm

atio

n gi

ven.

AN

S: D

T

OP

: C

ompl

emen

t rul

e

26. U

se S

cena

rio 5

-2. T

he p

roba

bilit

y th

at y

ou d

raw

eith

er a

bro

wn

or a

gre

en c

andy

is

' \:

Add

ition

of d

isjo

int

even

ts

6.E

).7.

AN

S: C

92C

hapt

er 5

: Pro

babi

lity

: Wha

t ar

e th

e C

hanc

es?

27. H

ere

is a

n as

sign

men

t of

prob

abil

itie

s to

the

face

tha

t com

es u

p w

hen

roll

ing

a di

e on

ce:

~~"

\ Out

com

eP

roba

bilit

y]/

X/7

2 2/7

3 JL

^4 3/

75 0

6 1/7

=

7/7

-

Whi

ch o

f th

e fo

llow

ing

is tr

ute?

Ayf

his

isn'

t a le

giti

mat

e si

gnm

ent

oCrj

roba

bilit

y^ b

ecau

se e

vehs

^ace

of

a di

e m

ust h

ave p

roba

bili

ty

. .

\ °*

- .

l£)f

This

isn

't a

legi

timat

e as

srgn

men

t of

prob

abil

ity,

bec

ause

it g

ives

pro

babi

lity

zero

to r

olli

ng a

3 or

a 5.

Sfc

UI*Y

£ K

.e>/

<~/

\ \s

isn'

t a

legi

timat

e as

sign

men

t of

pro

babi

lity,

bec

ause

the

prob

abili

ties

do n

otjid

^Ho

exac

tly 1

.

Thi

s is

n't a

legi

timat

e as

sign

men

t of

prob

abil

ity,

bec

ause

we

mus

£^cf

ually

rol

fthe

die

man

y tim

esle

arn

the

true

pro

babi

liti

es.

Ey

rhis

is

a .le

gitim

ate

assi

gnm

ent

f pr

obab

ilit

y.S

: E /

T

OP:

Bas

ic P

roba

bilit

y R

ules

28. S

tude

nts

at U

nive

rsity

Xm

ust h

ave

one

of f

our

clas

s ra

nks—

fres

hman

, so

phom

ore,

juni

or, o

r se

nior

.A

t Uni

vers

ity^

, 35%

of t

he s

tude

nts

are

fres

hmen

and

30%

are

joph

omor

es.

If a

Uni

vers

ity X

stu

dent

is

sele

cted

at r

ando

m, t

he p

foba

bllr

tyth

at I

vTor

she

is e

ithe

r a

juni

or o

r a

seni

or is

C)

65%

.D

) 70

%.

E)

89.5

%.

AN

S: B

TO

P: A

ddit

ion

of d

isjo

int

even

ts

29. I

f th

e kn

owle

dge

that

an

even

t A h

as o

ccur

red

impl

ies

that

a s

econ

d ev

ent B

can

not o

ccur

, the

eve

nts

A a

nd B

are

sai

d to

be

A) i

ndep

ende

nt.

j (1

3) d

isjo

int.

Vic

,^

't^

mut

uall

yvex

haus

tive

7)D

) the

sam

ple

spac

e.E

) co

mpl

emen

tary

.A

NS:

B

TO

P: M

utua

lly e

xclu

sive

eve

nts

Lfce

the

follo

win

g fo

r qu

estio

ns 3

0 -

32:

Scen

ario

5-3

Igno

ring

twin

s an

d ot

her

mul

tipl

e bi

rths

, ass

ume

that

bab

ies

born

at a

hos

pita

l are

inde

pend

ent r

ando

mev

ents

with

the

prob

abil

ity

that

a b

aby

is a

boy

and

the

prob

abil

ity

that

a b

aby

is a

gir

l bot

h eq

ual t

o 0.

5.

30. U

se S

cena

rio

5-3.

The

pro

babi

lity

that

the

next

fiv

e ba

bies

are

gir

ls is

A)

1.0.

^B

)0.5

. [

QO

.l.

(j DJ

. -

D^O

.062

5.(S

p).0

3125

.A

NS

:E

TO

P: M

ulti

plic

atio

n R

ule,

Ind

epen

dent

eve

nts

The

Prac

tice

of S

tatis

tics

for A

P*, 4

th e

ditio

n93

31. U

se S

cena

rio

5-3.

The

pro

babi

lity

that

at l

east

one

of t

he n

ext t

hree

bab

ies

is a

boy

isA

) 0.

1 25.

, —

8)0.

333.

?

Cn

TO

P: C

ompl

emen

t ru

le

32. U

se S

cena

rio

5-3.

The

eve

nts

A =

the

next

two

babi

es a

re b

oys,

and

B =

the

next

two

babi

es a

re g

irls

A)

disj

oint

, j

^HB

) co

nditi

onal

.C

) ind

epen

dent

.D

) co

mpl

emen

tary

.E

) on

e of

the

abov

e.A

NS:

A

TO

P: M

utua

lly e

xclu

sive

eve

nts

33. E

vent

A o

ccur

s w

ith p

roba

bili

ty 0

.3. I

f ev

ents

and

B a

re d

isjo

int,

then

C)P

(B)<

0.7.

D)P

(£)>

0.7.

AN

S: C

T

OP:

Mut

ually

exc

lusi

ve e

vent

s

34. A

sta

ck o

f fo

ur c

ards

con

tain

s tw

o re

d ca

rds

and

two

blac

k ca

rds.

I s

elec

t tw

o ca

rds,

one

at a

tim

e,an

d do

not

rep

lace

the

fir

st c

ard

sele

cted

bef

ore

sele

ctin

g th

e se

cond

car

d. C

onsi

der

the

even

ts^

2 «

^"

A =

the f

irst

card

sel

ecte

d is

red

U

/i &

^

^

B =

the

seco

nd c

ard

sele

cted

is

red

~--

\ )

5l_A

c.v(

The

eve

nts

A a

nd B

are

^N

^

^ ?^

T - ^

) c

T>

7c>

A)

inde

pend

ent a

nd d

isjo

int.

~B

) no

t in

depe

nden

t, bu

t di

sjoi

nt.

C)

inde

pend

ent,

not d

isjo

int

©^ot

inde

pend

ent,

not d

isjo

int.

E)

inde

pend

ent,

but w

e ca

n't t

ell

it's

disj

oint

with

out f

urth

er i

nfor

mat

ion.

~p

>A

NS:

D

TO

P: I

ndep

ende

nt a

nd m

utua

lly e

xclu

sive

eve

nts

Whi

ch o

f th

e fo

llow

ing

stat

emen

ts is

not

tru

e?A

) If

two

even

ts a

re m

utua

lly

excI

usiv

eTth

ey a

re n

ot in

depe

nden

t. "T

^ \

"^^T

B) I

f tw

o ev

ents

are

mut

uall

y ex

clus

ive,

then

P(A

r\B

) =

Q "

T"

—

\—C

yjf

two

even

ts a

re in

depe

nden

t, th

en th

ey m

ust b

e m

utua

lly

excl

usiv

e. F

'

D)

If tw

o ev

ents

, A a

nd B

, are

inde

pend

ent,

then

^^

/^s-

:-

- —

~\

( A

NS:

C

TO

P: I

ndep

ende

nt a

nd m

utua

lly

excl

usiv

e ev

ents

94

Cha

pter

5: P

roba

bilit

y: W

hat

are

the

Cha

nces

?

36. I

n a

cert

ain

tow

n, 6

0% o

f th

e ho

useh

olds

hav

e br

oadb

and

inte

rnet

acce

ss, 3

0% h

ave

at le

ast

one

high

-de

fini

tion

tel

evis

ion,

and

20%

hav

e bo

th.

The

pro

port

ion

of h

ouse

hold

s th

at h

ave

neith

er_b

road

band

inte

rnet

or

high

-def

initi

on t

elev

isio

n is

:

, -30

-.E

) 90

%.

AN

S: C

T

OP:

Gen

eral

add

itio

n ru

le

J 37

. Sup

pose

that

A a

nd B

are

inde

pend

ent e

vent

s w

ith

P(A

) =

0.2

and

P(B

] =

0.4

.

A)

0.08

. .=

q

/B

)0.1

2.

^ +

'

TO

P: G

ener

al a

ddit

ion

rule

(an

d m

ulti

plic

atio

n of

inde

p. e

vent

s)

38. S

uppo

se th

at A

and

B a

re in

depe

nden

t eve

nts

wit

h P

(A^)

= 0

.2 a

nd P

(B}

= 0

.4 .

D)

0.52

.E

) 0.

60.

AN

S: B

T

OP:

Mul

tipl

icat

ion

Rul

e, I

ndep

ende

nt e

vent

s; C

ompl

emen

t

Use

the

follo

win

g to

ans

wer

que

stio

ns 3

9 -

40:

Scen

ario

5-4

In a

par

ticu

lar

gam

e, a

fai

r di

e is

toss

ed.

If th

e nu

mbe

r of

spo

ts s

how

ing

is e

ithe

r fou

r or

fiv

e, y

ou w

in $

1 .If

the

num

ber

of s

pots

sho

win

g is

six

, you

win

$4.

And

if t

he n

umbe

r of

spo

ts s

how

ing

is o

ne, t

wo,

or

thre

e, y

ou w

in n

othi

ng. Y

ou a

re g

oing

to p

lay

the

gam

e tw

ice.

t>T

ce

.39

. Use

Sce

nari

o 5-

4. T

he p

roba

bili

ty th

at y

ou w

in $

4 bo

th ti

mes

isA

) 1/

36.

/v

t~

~^~7

77"

-t-o

C)

1/6.

D)l

/4.

3

E)1

/3'

vA

NS:

A

TO

P: M

ulti

plic

atio

n R

ule,

Ind

epen

dent

eve

nts

' 5

The

Pra

ctic

e of

Sta

tistic

s fo

r A

P*, 4

th e

ditio

n 95

40. U

se S

cena

rio

5-4.

The

pro

babi

lity

that

you

win

at l

east

$1

both

tim

es is

A) 1

/36.

"

<B

X4/

36.

D)

1/2.

E)

3/4.

AN

S: C

T

OP:

Mul

tipl

icat

ion

Rul

e, I

ndep

ende

nt e

vent

s;

Com

plem

ent

Use

the

follo

win

g to

ans

wer

que

stio

ns 4

1 -

43:

Scen

ario

5-5

Supp

ose

we

roll

two

six-

side

d di

ce—

one

red

and

one

gree

n. L

et^4

be

the

even

t tha

t the

num

ber o

f sp

ots

show

ing

on th

e re

d di

e is

thre

e or

less

and

B b

e tii

e~ev

ehTt

hat t

he n

umbe

r of

spot

s sh

owin

g on

the

gree

ndi

e is

thre

e or

mor

e.

41. U

se S

cena

rio 5

-5. T

he e

vent

s A a

nd B

are

A)d

isjo

int. fri^

GA

e^

t 3

B)

cond

itio

nal.

(C))

inde

pend

ent.

D)

reci

proc

als.

E)

com

plem

enta

ry.

AN

S: C

T

OP:

Ind

epen

dent

and

mut

ually

exc

lusi

ve e

vent

s

. Use

Sce

nari

o 5-

5. P

(A n

B) =

A)

1/6.

G^tt

^ 3-1.

A'C

M/3

. (*

|)^D

)5/6

.E

) no

ne o

f the

se.

AN

S:C

TO

P: M

ulti

plic

atio

n R

ule,

Ind

epen

dent

eve

nts

|43.

Use

Sce

nari

o 5-

5. P

(AA

) 1/

6.B

) 1/

4.Q

2/3

.s^

~~

\ .

_

±L ^o

AN

S: D

TO

P: G

ener

al a

ddit

ion

rule

(and

mul

tipl

icat

ion

of in

dep

. eve

nts)

96C

hapt

er 5

: Pro

babi

lity:

Wha

t are

the

Cha

nces

?

Use

the

follo

win

g to

ans

wer

que

stio

ns 4

4 -

46:

Scen

ario

5-6

A s

yste

m h

as tw

o co

mpo

nent

s tha

t ope

rate

in

para

llel

, as

show

n in

the

diag

ram

bel

ow. B

ecau

se t

heco

mpo

nent

s op

erat

e in

par

alle

l, at

lea

st o

ne o

f the

com

pone

nts

mus

t fun

ctio

n pr

oper

ly if

the

syst

em i

s to

func

tion

prop

erly

. L

et F

den

ote

the

even

t tha

t com

pone

nt 1

fail

s du

ring

one

per

iod

of o

pera

tion

and

Gde

note

the

even

t th

at c

ompo

nent

2 f

ails

dur

ing

one

peri

od o

f op

erat

ion.

Sup

pose

P(F

) =

0.2

0 an

d

= 0

.03.

The

com

pone

nt fa

ilure

s ar

e ind

epen

dent

./•

._\

( F

J -,

Inpu

tO

utpu

t

44. U

se S

cena

rio

5-6.

The

eve

nt c

orre

spon

ding

to

the

syst

em f

ailin

g du

ring

one

per

iod

of o

pera

tion

is

9/^

~r\\

F^

rjr

/-~

'^>

-^

-—

T~U

/--

^M

<^T

F A

A

P A

< i-

I^

J

Hr&

/v^

T^

K c

i ~rH

C

-O »

»A «

°«//^

t-

(TS

s /

~'

( A

) f

ana

(_/•.

C.o

r>\P

dv£

/^m

1

2- .

C) n

ot F

or n

ot G

.D

) no

t F a

nd n

ot G

.E

) no

t F o

r G.

AN

S:A

T

OP:

Int

erse

ctio

n of

eve

nts

45. U

se S

cena

rio

5-6.

The

eve

nt c

orre

spon

ding

to th

e sy

stem

fun

ctio

ning

pro

perl

y du

ring

one

per

iod

ofop

erat

ion

is

4 «

/g)n

ot F

orn

olG

DD

) not

F an

d no

t G.

E)n

otF

orG

.A

NS:

C

TO

P: U

nion

of

even

ts

46. U

se S

cena

rio

5-6.

The

pro

babi

lity

that

the

syst

em f

unct

ions

pro

perl

y du

ring

one

per

iod

of o

pera

tion

is

. A

T

L-E

Pss

T

^

0>

*<

>a

m*

JV

>

"O

ST

^^

X

C) o

:940

.'D

) 0.

970.

)T

OP:

Mul

tipl

icat

ion

Rul

e, I

ndep

ende

nt e

vent

sA

NS

:E

The

Pra

ctic

e of

Sta

tistic

s fo

r A

P*,

4th

editi

on97

47. E

ven

ts o

ccur

s w

ith

prob

abil

ity

0.8.

The

con

diti

onal

pro

babi

lity

that

eve

nt B

occ

urs,

giv

en th

at A

occu

rs,

is 0

.5. T

he p

roba

bilit

y th

at b

oth

A a

nd B

occ

ur

P/V

"")

= •

%

'p

( t?

>l

A^

- 5"

A)

is 0

.3.

—

~ -?

ft

is 0

.625

.-B

fiS

US

TE

) ca

nnot

be

dete

rmin

ed fr

om th

e in

form

atio

n gi

ven.

AN

S: B

TO

P: C

ondi

tion

al p

roba

bilit

y fo

rmul

a

| 48

. Eve

nt^

occu

rs w

ith

prob

abil

ity

0.3,

and

even

t B o

ccur

s w

ith

prob

abil

ity

0.4.

If A

and

5 a

rein

depe

nden

t, w

e m

ay c

oncl

ude

that

-

•>.

A)P

(Jan

d5

) =

0.1

2v(-

^(.

4) •/

V

(.f

t)

a , 3

ofr

S

B) P

(J|5

) =

0.3

.-

D)

all

of th

e ab

ove.

E) n

one

of th

e ab

ove.

AN

S: D

TO

P: C

ondi

tion

al p

roba

bilit

y fo

rmul

a

49. T

he c

ard

gam

e E

uchr

e us

es a

dec

k w

ith 3

2 ca

rds:

Ace

, R

ing,

Que

en, J

ack.

10,

9, 8

, 1 o

f ea

ch s

uit.

Supp

ose

you

choo

se o

ne c

ard

at r

ando

m f

rom

a w

ell-

shuf

fled

Euc

hre

deck

. W

hat i

s th

e pr

obab

ility

that

the

card

is

a Ja

ck,

give

n th

at y

ou k

now

it's

a fa

ce c

ard?

"B

)l/4

C)l

/8D

)l/9

E) 1

/12

AN

S: A

TO

P: C

ondi

tion

al p

roba

bilit

y fo

rmul

a

T

98C

hapt

er 5

: Pro

babi

lity:

Wha

t are

the

Cha

nces

?

50. A

plu

mbi

ng c

ontr

acto

r pu

ts i

n bi

ds o

n tw

o la

rge

jobs

. Let

A =

the

even

t tha

t the

con

trac

tor w

ins t

hefi

rst

cont

ract

and

let

B =

the

even

t tha

t the

con

trac

tor

win

s the

sec

ond

cont

ract

. W

hich

of t

he f

ollo

win

gV

enn

diag

ram

s has

cor

rect

ly s

hade

d th

e ev

ent t

hat t

he c

ontr

acto

r win

s ex

actly

one

of

the

cont

ract

s?

A)

B)

<t>

VJ^

K*^z

)^

7x ^%

RS

#f

1B

AS \)

D)

AN

S:C

TO

P: V

enn

diag

ram

s

The

Pra

ctic

e of

Sta

tistic

s fo

r AP*

, 4t

h ed

ition

99

51. A

mon

g th

e st

uden

ts a

t a la

rge

univ

ersi

ty w

ho d

escr

ibe

them

selv

es a

s ve

geta

rian

s, s

ome

eat f

ish,

som

eea

t egg

s, s

ome

eat b

oth

fish

and

eggs

, and

som

e ea

t nei

ther

fish

nor

egg

s. C

hoos

e a

vege

taria

n st

uden

t at

rand

om.

Let

E =

the

even

t tha

t the

stu

dent

eat

s eg

gs, a

nd le

t F =

the

even

t tha

t the

stu

dent

eat

s fi

sh.

Whi

ch o

f the

fol

low

ing

Ven

n di

agra

ms

has

corr

ectly

sha

ded

the

even

t th

at th

e st

uden

t eat

s ne

ithe

r fis

h no

reg

gs? A)

, =

N^

,

B)

C)

E)

D)

AN

S:A

TO

P: V

enn

diag

ram

s

100

Cha

pter

5: P

roba

bili

ty: W

hat

are

the

Cha

nces

?

Use

the

follo

win

g fo

r qu

estio

ns 5

2 -

53

:

Scen

ario

5-7

The

pro

babi

lity

of a

rand

omly

sel

ecte

d ad

ult h

avin

g a

rare

dis

ease

for

whi

ch a

dia

gnos

tic t

est h

as b

een

deve

lope

d is

0.0

01. T

he d

iagn

osti

c te

st is

not

per

fect

. The

pro

babi

lity

the

test

wil

l be

pos

itive

(in

dica

ting

that

the

pers

on h

as th

e di

seas

e) i

s 0.

99 f

or a

per

son

with

the

dis

ease

and

0.0

2 fo

r a p

erso

n w

itho

ut th

edi

seas

e.

52. U

se S

cena

rio

5-7.

The

pro

port

ion

of a

dult

s fo

r w

hich

the

test

wou

ld b

e po

sitiv

e is

A)

0.00

002.

B)

0.00

099.

C)

0.0

1998

. . -„

0.02

097D

.Q

OC

flT

-f-

,0| W

TO

P: M

ulti

plic

atio

n ru

le, d

epen

dent

eve

nts

AN

S: D

53. U

se S

cena

rio

5-7.

If

a ra

ndom

ly s

elec

ted

pers

on i

s te

sted

and

the

resu

lt is

pos

itive

, th

e pr

obab

ility

the

indi

vidu

al h

as th

e di

seas

e is

TV

- \-

~\

f T^

>^ <

• a^c

A)

0.00

1.

HD

lStT

Ast

r \T

£S

T.^

)^

?(1

>^

A^

B)

0.01

9.C

) 0.

020.

D)

0.02

1.I 0

.047

'!_T

OP:

Con

ditio

nal

prob

abili

ty f

orm

ula

,o/

D^*

^ X

^^

'°MH

\o^

The

Prac

tice

of S

tatis

tics

for A

P*, 4

th e

ditio

n10

1

Use

the

follo

win

g fo

r qu

estio

ns 5

4 —

57:

Scen

ario

5-8

A s

tude

nt is

cho

sen

at r

ando

m fr

om t

he R

iver

City

Hig

h Sc

hool

stu

dent

bod

y, a

nd th

e fo

llow

ing

even

tsar

e re

cord

ed:

M =

The

stu

dent

is

mal

eF

= T

he s

tude

nt is

fem

ale

B =

The

stu

dent

ate

bre

akfa

st t

hat m

orni

ng.

N =

The

stu

dent

did

not

eat

bre

akfa

st t

hat m

orni

ng.

The

fol

low

ing

tree

dia

gram

giv

es p

roba

bilit

ies

asso

ciat

ed w

ith t

hese

eve

nts.

54. U

se S

cena

rio

5-8.

Wha

t is

the

prob

abil

ity

that

the

sele

cted

stu

dent

is

a m

ale

and

ate

brea

kfas

t?

B)0

.40

C)

0.50

D)

0.64

E)

0.80

AN

S: A

TO

P: P

roba

bilit

ies

from

tre

e di

agra

m

Use

Sce

nari

o 5-

8. W

hat

is th

e pr

obab

ility

that

the

stud

ent h

ad b

reak

fast

?A

) 0.

32

E)

0.80

AN

S: C

TO

P: P

roba

bilit

ies

from

tre

e di

agra

m

6. U

se S

cena

rio

5-8.

Giv

en th

at a

stu

dent

who

ate

bre

akfa

st i

s se

lect

ed, w

hat i

s th

e pr

obab

ility

that

he

is

0)0

.64

rsoA

NS:

DT

OP:

Pro

babi

litie

s fr

om t

ree

diag

ram

102

Cha

pter

5: P

roba

bilit

y: W

hat a

re th

e C

hanc

es?

Use

Sce

nari

o 5-

8. F

ind

P^B

1 F

) an

d w

rite

in w

ords

wha

t thi

s ex

pres

sion

re

pres

ents

.

A)

0.18

; The

pro

babi

lity

the

stud

ent a

te b

reak

fast

and

is

fem

ale.

B)

0.18

; The

pro

babi

lity

the

stud

ent a

te b

reak

fast

, giv

en s

he i

s fe

mal

e.C

) 0.

18; T

he p

roba

bilit

y th

e st

uden

t is

fem

ale,

giv

en s

he a

te b

reak

fast

.0.

30;

The

pro

babi

lity

the

stud

ent a

te b

reak

fast

, gi

ven

she

is f

emal

e.0.

30;

The

pro

babi

lity

the

stud

ent

is fe

mal

e, g

iven

she

ate

bre

akfa

st.

AN

S: D

T

OP

: P

roba

bilit

ies

from

tre

e di

agra

m

Use

the

follo

win

g fo

r qu

estio

ns 5

8-59

:

Scen

ario

5-9

You

ask

a s

ampl

e of

370

peo

ple,

"Sh

ould

cli

nica

l tri

als

on i

ssue

s su

ch a

s he

art

atta

cks

that

aff

ect

both

sexe

s us

e su

bjec

ts o

f ju

st o

ne s

ex?"

The

resp

onse

s ar

e in

the

tabl

e be

low

.

Supp

ose

you

choo

se o

ne o

f the

se p

eopl

e at

ran

dom

Yes

No

Mal

eFe

mal

e34 46

105

185

23

!

58. U

se S

cena

rio

5-9.

Wha

t is

the

prob

abili

ty t

hat t

he p

erso

n sa

id "

Yes

," g

iven

tha

t sh

e is

a w

oman

?

B) 0

.22

C)

0.25

D)

0.50

E)

0.57

5A

NS:

AT

OP:

Con

diti

onal

pro

babi

lity

from

2-w

ay t

able

59. U

se S

cena

rio

5-9.

Wha

t is

the

prob

abili

ty th

at th

e pe

rson

is

a w

oman

, giv

en th

at s

he s

aid

"Yes

?"A)

0.20

B)0

.22

C) 0

.25

D)

1J)0

.575

JfS

7lf

T

OP

: Con

diti

onal

pro

babi

lity

from

2-w

ay t

able

The

Pra

ctic

e of

Sta

tist

ics

for

AP

*, 4

th e

diti

on10

3

60. E

ach

day,

Mr.

Bay

ona

choo

ses

a on

e-di

git n

umbe

r fro

m a

ran

dom

num

ber t

able

to

deci

de if

he

will

wal

k to

wor

k or

dri

ve th

at d

ay.

The

num

bers

Oth

roug

h 3

indi

cate

he

wiiL

driv

e. 4

thro

ugh

9 m

ean

he w

ill

wal

k. I

f he

driv

es,

he h

as a

pro

babi

lity

of

0.1

of b

eing

late

. If

he

wal

ks, h

is p

roba

bili

ty o

f be

ing

late

rise

s"t

o^i.2

5.

Let

W =

Wal

k, D

= D

rive

, L =

Lat

e, a

nd N

L =

Not

Lat

e.

Whi

ch o

f the

fol

low

ing

tree

dia

gram

ssu

mm

ariz

es th

ese

prob

abili

ties?

A)

c) E)

NL

D)

AN

S:A

TO

P:

Tre

e di

agra

m fr

om p

roba

bili

ties

Use

the

foll

owin

g fo

r qu

esti

ons

61 -

62.

104

Cha

pter

5: P

roba

bilit

y: W

hat a

re th

e C

hanc

es?

Scen

ario

5-1

0

The

Ven

n di

agra

m b

elow

des

crib

es t

he p

ropo

rtio

n of

stu

dent

s w

ho t

ake

chem

istr

y an

d Sp

anis

h at

Jeff

erso

n H

igh

Scho

ol,

Whe

re A

= S

tude

nt ta

kes

chem

istr

y an

d B

= S

tude

nts

take

s Sp

anis

h.

Supp

ose

one

stud

ent i

s ch

osen

at r

ando

m.

B

61. U

se S

cena

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5-10

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nd th

e va

lue

of P

[A ^

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nd

desc

ribe

it in

wor

ds.

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dent

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1; T

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bili

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at th

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t tak

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ither

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or S

pani

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ut n

ot b

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(DM

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62. U

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cena

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babi

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enn

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e of

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105

Use

the

follo

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r qu

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3 -

65:

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1

The

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hand

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0 C

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63. U

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t is

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abili

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64. U

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5-11

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now

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as b

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wha

t is

the

prob

abili

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refe

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com

mun

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65. U

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5-11

. Whi

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f th

e fo

llow

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stat

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uppo

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the

conc

lusi

on th

at th

e ev

ent "

Rig

ht-

hand

ed"

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the

even

t "O

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or q

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66

- 68

:

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nari

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12

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Ven

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s th

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the

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cena

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67. U

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cena

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r +

s

q +

r +

sA

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:DT

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n di

agra

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68. U

se S

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5-12

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ty a

ssoc

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he i

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of A

and

B.

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enn

diag

ram

s

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tice

of S

tatis

tics f

or A

P*, 4

th e

ditio

n10

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the

follo

win

g fo

r qu

estio

ns 6

9— 7

1:

Scen

ario

5-1

3

One

hun

dred

hig

h sc

hool

stud

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wer

e as

ked

if th

ey h

ad a

dog

, a c

at, o

r bot

h at

hom

e. H

ere

are

the

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lts.

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otal

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69. U

se S

cena

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5-1 3

. If a

sin

gle

stud

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s se

lect

ed a

t ran

dom

and

you

know

she

has

a d

og, w

hat i

s th

epr

obab

ility

she

als

o ha

s a

cat?

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70. U

se S

cena

rio

5-13

. If

a si

ngle

stud

ent

is s

elec

ted

at ra

ndom

, wha

t is

the

prob

abili

ty a

ssoc

iate

d w

ith t

heun

ion

of th

e ev

ents

"ha

s a

dog"

and

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ondi

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roba

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om 2

-way

tab

le

71. U

se S

cena

rio

5-13

. If t

wo

stud

ents

are

sele

cted

at r

ando

m, w

hat i

s the

pro

babi

lity

that

nei

ther

of t

hem

has

a do

g or

a c

at?

A) 0

.37

B)J

L54

D)

0.65

5E

) 0.7

4A

NS:

CT

OP:

Con

diti

onal

pro

babi

lity

from

2-w

ay t

able

108

Cha

pter

5: P

roba

bilit

y: W

hat a

re th

e Cha

nces

?