11.7 use geometric probability notes · 2018-04-18 · 4 2 0 2 4 6 8 10 12 l m n p o n lj s is o n...

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304 L es son 11 . 7 · G Æy N o te b n g e de Co py ri g ht © M cDou g a l L itte \ı / Hou h to n M ifn in C om p an y . I L - - ı ' ' " " " '" " " " ' L e. G th of Ľ L e n g th of i È ĦI rr x .. . = : w w w Fi n d th e p ro b a b ı t y th at a w »ı n t c hosen at random E x am p \ e ı U s e ıe n g th s to fın d a g e om e tric p ro ba b iıit y B P ( K i s on C D to the ı e n g th o f A B . ra tı o o f th e le n g th of th a t It is o n C D is th e th en the p ro b a b ilit y ch o s e n a t ra ndom , ı f a p o in t K o n A B is L e t A B be a seent th at c o n ta ı ns the se g m e n t C D . PROBABı U TY A N D LENGTH G eom e tri c p ro b a b iı it y P ro b a b ilit y VOCA BULARY p ro b a b iı it ı es . : · G oa í J · U se ı en g ths and a re a s to fin d g eom e tric Vb u r N o te s P 甲 W l U se G e o m e tric P robabiıit y p p rn

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Page 1: 11.7 Use Geometric Probability Notes · 2018-04-18 · 4 2 0 2 4 6 8 10 12 L M N P o n Lj s is o n )ii Ñ. 1. ... 11.7 Use Geometric Probability Notes Author: CamScanner Subject:

3 0 4 L e s s o n 1 1 . 7 · G Æ y N o te b k ın g e u ıd e C o p y rig h t © M c D o u g a l L itte \ı/ H o u � h to n M ifn in C o m p a n y .

IL - - lıı' ' " " " ' " " " "

'

L e . G th o f ĽL e n g t h o fiÈĦI rr x . . . =

: w w w

F in d t h e p ro b a b ılıt y t h a t a w »ın t c h o s e n a t ra n d o m

E x a m p \ e ı U s e ıe n g t h s t o f ın d a g e o m e tr ic p r o b a b iıity

B

P (K is o nC D to t h e ıe n g th o f A B .

ra tıo o f t h e le n g th o f

th a t It is o n C D is t h e

th e n t h e p ro b a b ility

c h o s e n a t ra n d o m ,

ıf a p o in t K o n A B is

L e t A B b e a s e e n t th a t c o n t a ın s t h e s e g m e n t C D .

P R O B A B ıU T Y A N D L E N G T H

G e o m e t ric p ro b a b iıity

P ro b a b ility

V O C A B U L A R Y

p ro b a b iıitıe s .

: · G o a í J · U s e ıe n g th s a n d a re a s t o f in d g e o m e t ric

Vb u r N o t e s

P 甲 W l U s e G e o m e t r ic P r o b a b iıit y

p p r n

Page 2: 11.7 Use Geometric Probability Notes · 2018-04-18 · 4 2 0 2 4 6 8 10 12 L M N P o n Lj s is o n )ii Ñ. 1. ... 11.7 Use Geometric Probability Notes Author: CamScanner Subject:

C o p y rig h t © M c D o u g a l u tte ll/ H o u g h to n M itftín C o m p a n y . L e s s o n 1 1 . 7 ·

G a a m e t ry N k l n g G ıııd e 3 0 5

P (K is in re g io n M ) =

o f J .

re g io n M is t h e ra t io o f t h e a re a o f M to t h e a re a

J is c h o s e n a t ra n d o m , t h e n t h e pr o b a b i l i t y t h a t i t i s i n

L e t j b e a re g ıo n t h a t c o n ta ın s re g io n M . ıf a p o ın t K ın

P R O B A B ıU T Y A N D A R E A

o r % .

T h e p ro b a b ılıt y t h a t y o u g e t to to w n b y 2 : 5 7 is

M a x ım u m w a ltın g tım e

F a v o ra b ıe w a ltın g t im e

P (G e t to to w n b y 2 5 7 )

S te p 3 F ın d t h e p ro b a b llıty .

T h e s h u tt le n e e d s t o a rriv e w ith in t h e f irs t m in u t e s .

M in u t e s w a it in g 0 2 4 6 8 1 0 1 2 1 4 1 6

T im e 2 :4 1 2 4 3 2 :4 5 2 :4 7 2 4 9 2 5 1 2 :5 3 2 5 5 2 :5 7

Y o u n e e d It t o a r riv e w lt h ln m ın u t e s .

1 0 m in u t e s , s o I t w i l l a r r i v e I n 1 0 m ın u t e s o r l e s s .

M o d e l t h e s ıt u a t io n . T h e s h u tt le ru n s e v e ryS te p 2

(_

- 2 : 4 1 = m ın ).

T h e lo n g e s t y o u c a n w a it ıs m in u te s

n o la t e r t h a n 1 3 m ın u te s b e fo re 2 : 5 7 , o r .

1 3 m in u te s , s o y

o u n e e d t o c a t c h t h e s h u t t l e

s tııl g e t t o t o w n b y 2 5 7 . T h e rıd e ta k e s

F ın d t h e lo n g e s t y o u c a n w a ıt fo r t h e s h u tt le a n dS te p 1

s o ıu t io n

y o u w ill g e t t h e re b y 2 : 5 7 ?

Y o u w a n t t o g e t to to w n b y 2 5 7 . W h a t is t h e p ro b a b ility

O n e a fte rn o o n , yo u a r r i v e a t t h e b o a r d ın g ıo c a tıo n a t 2 4 1 .

fro m y o u r b o a rd in g lo c a tıo n to t o w n ta k e s 1 3 m in u t e s .

S h u td e A s h u tt le to t o w n ru n s e v e r y ĺ o m in u t e s . T h e r id e

E x a m p \ e 2 a s e g m e n t to m o d e ı a re a l-

w o r ld p ro b ay o u r N o te s

Page 3: 11.7 Use Geometric Probability Notes · 2018-04-18 · 4 2 0 2 4 6 8 10 12 L M N P o n Lj s is o n )ii Ñ. 1. ... 11.7 Use Geometric Probability Notes Author: CamScanner Subject:

T h e p ro b a b iııty t h a t a p rız e ls w o n ıs , o r % .

3 0 6 L e s s o n 1 1 . 7 ·

G o o m My

N o t a t ı k ıng

G u ıd e C op w

ig

h t © M c D o ug

a ı L i « e l l/ H o u g h to n M IM In C o m p a n y .

ın t h e h o le .

ın d ia m e te r. F in d th e p ro b a b ilıty t h a t y o u r b a ıı s t o p s

O n t h e g re e n in E x a m p ıe 3 , t h e h o ıe is 4 . 2 5 in c h e s3 .

w ill g e t t o t o w n b y 2 : 5 7 ?

lo c a t io n a t 2 3 8 . W h a t ls th e p ro b a b ility t h a t y o u

ın E x a m p ıe 2 , s u p p o s e y

o u a r r ıv e a t t h e p ıc k up2 .

4 2 0 2 4 6 8 1 0 1 2

L M N P

o n L js is o n )iiÑ .

1 . Fın d th e p ro b a b ıılt y t h a t a p o ın t c h o s e n a t ra n d o m

e c h e c *qp o ï ııt C o m p le t e t h e fo lıo w ın g e x e r c ıs e s .

he

s

t-

Ys o ıu t ıo n

ー ヘ

th a t a p r iz e is w o n ?

p o ın t o n t h e g re e n , w h a t i s t h e pr o b a b i l it

y

ıf th e b a ll is e q u a lly lık e ıy to s to p o n a n y

g re e n a n d c irc le a re s h o w n a t t h e rıg h t .

p a in t e d c irc le . T h e d ia m e te rs o f t h e

g re e n . A p rız e ıs w o n if it s to p s In t h e

'

G o ıf A g o lf b a ll is h lt a n d s to p s o n t h e

E x a m p \ e 3 a r e a s t o f in d a ge o m e tric p ro b a b iııY$b u r N o t e s

Page 4: 11.7 Use Geometric Probability Notes · 2018-04-18 · 4 2 0 2 4 6 8 10 12 L M N P o n Lj s is o n )ii Ñ. 1. ... 11.7 Use Geometric Probability Notes Author: CamScanner Subject:

S te p 2 F ın d t h e to ta ı a re a o f t h e p ro p e rty

th e a re a ls b lt = . = sq

u a r e u n i t s .

S te p 1 F ın d t h e g ra s s a re a . T h e s h a p e is a re c t a n g le , s o

s o ıu t ıo n

ıı国团ı国ı国团团ı国■国回 国

th e p ro b a b iıity t h a t It is o n g ra s s .

ıl G r a s s

ı

a n y w h e re o n t h e p ro p e rty , e s t i m a t e

ıl ı

» ı

is s h o w n in t h e s c a le d ra w in g .

§ IS ıı=

ıııı ■ııı■ı. · . ' - 一

国兰u ı I S ı 团 团 团 国

E x a m p \ e 4 E s t im a t e a r e a o n a g r id t o f in d a p r o b a b ilit y

C o p w ig h t © M c D o u g a l U tte ll/ H o u g h to n M iĦlln C o m p a n y . L e s s o n 1 1 . 7 · G e t r y N o te t a k in g G u ı 3 0 7

is ın t h e w a t e n

4 . In E x a m p le 4 , e s t ım a t e t h e p

r o b a b ıl ıty t h a t t h e d e e r

e Clï ec*poï nt C o m p le t e t h e fo ııo w ln g e x e rc ıs e .

H o m e m r k

fu ll s q u a re s .

g ra s s a n d in t h e

a re f u lly c o v e re d . T h e re

M a k e g ro u p s o f p a rt ia ı

w a te r. S o , t h e r e a r e

a re s q u a re s in t h e

C o u n t t h e s q u a re s t h a t