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...
TRANSCRIPT
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
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
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
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