HO

NO

RS

GE

OM

ET

RY

- C

HA

PT

ER

12

FIN

AL E

XA

M P

RE

PA

RA

TIO

N

N

AM

E:

__

__

__

__

__

__

__

__

__

__

__

__

HR

:__

__

_

1.

At

a sc

ho

ol

fest

ival

, a

colo

red

ch

ip i

s ra

nd

om

ly d

raw

n o

ut

of

a b

ag a

nd

rep

lace

d.

Th

e ta

ble

bel

ow

sh

ow

s th

e re

sult

s o

f 7

5 d

raw

s. E

stim

ate

the

pro

bab

ilit

y o

f ch

oo

sin

g a

gre

en c

hip

.

Outcome B

lue

Red

Gre

en

Pu

rple

G

old

Draws

18

14

16

8

1

9

a. 1

6%

c.

1

8.7

%

b. 2

1.3

%

d.

32

%

2. F

ind

th

e in

dic

ated

pro

bab

ilit

y

.

3.

A b

ag c

on

tain

s o

ran

ge,

wh

ite,

an

d p

urp

le m

arb

les.

If

yo

u r

and

om

ly c

ho

ose

a m

arb

le f

rom

th

e

bag

, th

ere

is a

23

% c

han

ce o

f d

raw

ing a

n o

ran

ge

mar

ble

an

d a

48

% c

han

ce o

f d

raw

ing a

wh

ite

mar

ble

. W

hat

is

the

pro

bab

ilit

y o

f ch

oo

sin

g a

pu

rple

mar

ble

? E

xpre

ss y

ou

r an

swer

as

a

per

cen

t.

a.

c.

71

%

b.

23

%

d.

29

%

4.

Fin

d t

he

pro

bab

ilit

y t

hat

a r

and

om

ly c

ho

sen

po

int

in t

he

circ

le a

lso

lie

s in

th

e eq

uil

ater

al

tria

ngle

.

a.

2

8%

c.

5

6%

b.

41

%

d.

45

%

5.

A g

rab

bag

co

nta

ins

2 f

oo

tbal

l ca

rds

and

8 b

ask

etb

all

card

s. A

n e

xp

erim

ent

con

sist

s o

f ta

kin

g

on

e ca

rd o

ut

of

the

bag

, re

pla

cin

g i

t, a

nd

th

en s

elec

tin

g a

no

ther

car

d.

Det

erm

ine

wh

eth

er t

he

even

ts a

re i

nd

epen

den

t. W

hat

is

the

pro

bab

ilit

y o

f se

lect

ing a

fo

otb

all

card

an

d t

hen

a

bas

ket

bal

l ca

rd? E

xp

ress

yo

ur

answ

er a

s a

dec

imal

.

a.

no

t in

dep

end

ent;

0.0

4

c.

no

t in

dep

end

ent;

0.6

4

b.

ind

epen

den

t; 0

.16

d

. in

dep

end

ent;

0.1

8

HO

NO

RS

GE

OM

ET

RY

- C

HA

PT

ER

12

FIN

AL E

XA

M P

RE

PA

RA

TIO

N

N

AM

E:

__

__

__

__

__

__

__

__

__

__

__

__

HR

:__

__

_

6.

Wh

at i

s th

e p

rob

abil

ity o

f ro

llin

g a

5 o

n t

he

firs

t n

um

ber

cub

e an

d r

oll

ing a

6 o

n t

he

seco

nd

nu

mb

er c

ub

e? A

ssu

me

the

nu

mb

er c

ub

es a

re f

air

and

hav

e si

x s

ides

. E

xp

ress

yo

ur

answ

er a

s a

frac

tio

n i

n s

imp

lest

fo

rm.

a.

c.

b.

d.

7.

Har

ry h

as 5

mar

ker

s in

a b

ackp

ack

. O

ne

of

them

is

pin

k a

nd

on

e is

gra

y.

Wh

at i

s th

e

pro

bab

ilit

y H

arry

wil

l re

ach

in

to t

he

bac

kp

ack

wit

ho

ut

loo

kin

g a

nd

gra

b t

he

pin

k m

ark

er a

nd

then

rea

ch i

n a

sec

on

d t

ime

and

gra

b t

he

gra

y m

ark

er i

f:

(a)

the

firs

t m

ark

er i

s not

rep

lace

d?

(b)

the

firs

t m

ark

er is r

epla

ced

?

Ex

pre

ss y

ou

r an

swer

s as

fra

ctio

ns

in s

imp

lest

fo

rm.

a.

(a)

(b)

c.

(a)

(b)

b.

(a)

(b)

d.

(a)

(b)

8.

A m

ov

ie c

om

pan

y s

ho

ws

on

e o

f it

s m

ov

ies

to a

gro

up

of

vie

wer

s b

efo

re t

he

mo

vie

is

rele

ased

.

Th

e re

sult

s o

f o

ne

sho

win

g a

re i

n t

he

tab

le.

Wh

at i

s th

e ap

pro

xim

ate

pro

bab

ilit

y t

hat

a p

erso

n i

s in

th

e 4

5-5

4 a

ge

gro

up

giv

en t

hat

th

ey

lik

ed t

he

mo

vie

?

a.

1

c.

0.3

5

b.

0.5

2

d.

0.1

8

HO

NO

RS

GE

OM

ET

RY

- C

HA

PT

ER

12

FIN

AL E

XA

M P

RE

PA

RA

TIO

N

N

AM

E:

__

__

__

__

__

__

__

__

__

__

__

__

HR

:__

__

_

9.

Th

e ch

ance

th

at a

pre

gn

ancy

res

ult

s in

tw

ins

is a

bo

ut

3%

. T

he

chan

ce t

hat

a p

regn

ancy r

esu

lts

in i

den

tica

l tw

ins

is a

bo

ut

0.3

%.

Giv

en t

hat

a p

reg

nan

cy r

esu

lts

in t

win

s, w

hat

is

the

pro

bab

ilit

y t

hey a

re i

den

tica

l tw

ins?

Ex

pre

ss y

ou

r an

swer

as

a p

erce

nt.

If

nec

essa

ry,

rou

nd

yo

ur

answ

er t

o t

he

nea

rest

ten

th o

f a

per

cen

t.

a.

10

%

c.

0.9

%

b.

3.3

%

d.

33

%

10

. Jo

yce

ask

ed 5

0 r

and

om

ly-s

elec

ted

stu

den

ts a

t h

er s

cho

ol

wh

eth

er t

hey h

ave

on

e o

r m

ore

bro

ther

s o

r si

ster

s. T

he

tab

le s

ho

ws

the

resu

lts

of

Joyce

’s p

oll

.

Mak

e a

tab

le o

f th

e jo

int

and

mar

gin

al r

elat

ive

freq

uen

cies

. E

xp

ress

per

cen

tag

es i

n d

ecim

al

form

.

a.

b.

c.

d.

HO

NO

RS

GE

OM

ET

RY

- C

HA

PT

ER

12

FIN

AL E

XA

M P

RE

PA

RA

TIO

N

N

AM

E:

__

__

__

__

__

__

__

__

__

__

__

__

HR

:__

__

_

11

. T

he

tab

le s

ho

ws

the

dis

trib

uti

on

of

mal

e an

d f

emal

e st

ud

ents

an

d l

eft-

an

d r

igh

t-h

and

ed

stu

den

ts i

n t

he

mat

h c

lub

. F

ind

th

e p

robab

ilit

y t

hat

a f

emal

e st

ud

ent

sele

cted

at

ran

do

m i

s

left

-han

ded

. E

xp

ress

yo

ur

answ

er a

s a

frac

tio

n i

n s

imp

lest

fo

rm.

Left-handed

Right-handed

Male

2

3

5

Female

6

3

6

a.

c.

b.

d.

12

. A

stu

dy c

om

par

ed t

he

on

-tim

e p

erfo

rman

ce f

or

thre

e b

us

com

pan

ies.

A t

able

wit

h t

he

join

t

and

mar

gin

al f

req

uen

cies

of

the

resu

lts

is s

ho

wn

.

Det

erm

ine

wh

ich

co

mp

any h

as t

he

bes

t o

n-t

ime

per

form

ance

. E

xp

lain

ho

w t

o i

den

tify

th

e

com

pan

y t

hat

per

form

ed b

est.

a.

C

ross

-Co

un

try B

us

has

th

e b

est

on

-tim

e p

erfo

rman

ce;

Div

ide

the

join

t re

lati

ve

freq

uen

cy o

f o

n-t

ime

arri

val

by t

he

mar

gin

al r

elat

ive

freq

uen

cy t

o f

ind

th

e b

est

per

form

ance

.

b.

Cro

ss-C

ou

ntr

y B

us

has

th

e b

est

on

-tim

e p

erfo

rman

ce;

Iden

tify

th

e g

reat

est

join

t

rela

tiv

e fr

equ

ency o

f o

n-t

ime

arri

val

s to

fin

d t

he

bes

t p

erfo

rman

ce.

c.

Red

Do

g T

ran

sit

has

th

e b

est

on

-tim

e p

erfo

rman

ce;

Div

ide

the

join

t re

lati

ve

freq

uen

cy o

f o

n-t

ime

arri

val

by t

he

mar

gin

al r

elat

ive

freq

uen

cy t

o f

ind

th

e b

est

per

form

ance

.

d.

Ex

pre

ss W

ay L

ines

has

th

e b

est

on

-tim

e p

erfo

rman

ce;

Div

ide

the

join

t re

lati

ve

freq

uen

cy o

f o

n-t

ime

arri

val

by t

he

mar

gin

al r

elat

ive

freq

uen

cy t

o f

ind

th

e b

est

per

form

ance

.

13

. T

he

sect

ion

s o

n a

sp

inn

er a

re n

um

ber

ed f

rom

1 t

hro

ugh

8.

If t

he

pro

bab

ilit

y o

f la

nd

ing o

n a

giv

en s

ecti

on

is

the

sam

e fo

r al

l th

e se

ctio

ns,

wh

at i

s th

e p

rob

abil

ity o

f sp

inn

ing a

nu

mb

er

less

th

an 4

or

gre

ater

th

an 7

in

a s

ingle

sp

in?

a.

b.

c.

d.

HO

NO

RS

GE

OM

ET

RY

- C

HA

PT

ER

12

FIN

AL E

XA

M P

RE

PA

RA

TIO

N

N

AM

E:

__

__

__

__

__

__

__

__

__

__

__

__

HR

:__

__

_

14

. A

mo

vie

co

mp

any s

urv

eyed

10

00

peo

ple

. 2

29

peo

ple

sai

d t

hey

wen

t to

see

th

e n

ew m

ov

ie

on

Fri

day,

25

6 s

aid

th

ey w

ent

on

Sat

urd

ay.

If 2

4 p

eop

le s

aw t

he

mo

vie

bo

th n

igh

ts,

wh

at i

s

the

pro

bab

ilit

y t

hat

a p

erso

n c

ho

sen

at

ran

do

m s

aw t

he

mo

vie

on

Fri

day o

r S

atu

rday?

a.

0.4

13

c.

0.4

61

b.

0.4

37

d.

0.4

85

15

. If

no

dig

it a

pp

ears

mo

re t

han

on

ce,

ho

w m

any 2

-dig

it n

um

ber

s ca

n b

e fo

rmed

fro

m t

he

dig

its

1,

3,

5,

and

7?

a.

12

b.

6

c.

16

d

. 4

16

. T

her

e ar

e 8

ru

nn

ers

in a

rac

e. W

hat

is

the

pro

bab

ilit

y t

hat

Ab

by,

Bec

ca,

and

Car

men

pla

ce

firs

t, s

eco

nd

, an

d t

hir

d i

n a

ny o

rder

?

a.

b.

c.

d.

17

. A

co

mm

itte

e is

to

co

nsi

st o

f tw

o m

emb

ers.

If

ther

e ar

e se

ven

peo

ple

av

aila

ble

to

ser

ve

on

th

e

com

mit

tee,

ho

w m

any d

iffe

ren

t co

mm

itte

es c

an b

e fo

rmed

?

a.

35

b.

21

c.

42

d

. 2

4

18

. W

hat

is

the

pro

bab

ilit

y t

hat

a p

oin

t se

lect

ed a

t ra

nd

om

in

th

e la

rge

rect

angle

wil

l b

e

con

tain

ed i

n e

ith

er t

he

squ

are

or

the

circ

le? R

ou

nd y

ou

r an

swer

to

th

e n

eare

st h

un

dre

dth

.

CH

12

AN

SW

ER

KE

Y: 1

) B

2) 0

.6

3)D

4

)B

5)B

6

)C

7)D

8

)C

9)A

1

0)A

1

1)B

1

2)A

1

3)A

1

4) C

1

5)A

1

6)B

1

7)B

1

8) 0

.37