Tugas Mat Presentasi Peluang

7/17/2019 Tugas Mat Presentasi Peluang

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>> 0 >> 1 >> 2 >> 3 >> 4 >>

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!


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DonDon

BoscoBoscoP I C T U R E SP I C T U R E S


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P R E S E NTS


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a

P R O P A B I L I T Y

X I S I E N E 1

" # s # n $ a $ % o n


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G R O U PG R O U P

22


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ARIO

ARI&ANDANA'ALI(


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EL)IN(AR&ADY


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*ARINAD&IYANI+A,ALI


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NIATANIA


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STE)ENTANI*O


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ELUAN

G


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S$an-a" *o.#$#nsI

(#n//naan a$"an s$a$%s$%aa%-a #ncacaan -an s%a$s%a$#an/ -aa. #.#caan .asaa


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*O(PETENSIDASAR

(#n//naan a$"an #"a%an

#".$as% -an o.%nas%-aa. #.#caan .asaa

(#n#n$an "an/ sa.#

sa$ #"coaan(#n#n$an #an/ sa$

#a-%an -an #nas%"ann:a


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L#$;s


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Kaidah

Pencacahan(#$o-# a%-a #ncacaan a-a 3 =

> $a#s%an/

> -%a/"a.oon

> #n/%s%an$#.a$:an/$#"s#-%a


27/85

contohtabelsilang2dadu

III 1 2 3 4 5 6

1 ?11@ ?12@ ?13@ ?14@ ?15@ ?16@

2 ?21@ ?22@ ?23@ ?24@ ?25@ ?26@

3 ?31@ ?32@ ?33@ ?34@ ?35@ ?36@

4 ?41@ ?42@ ?43@ ?44@ ?45@ ?46@

5 ?51@ ?52@ ?53@ ?54@ ?55@ ?56@

6 ?61@ ?62@ ?63@ ?64@ ?65@ ?66@


28/85

contohdiagrampohon2 KOIN

S%s% /a.a" +S%s% an/a A

o%n I o%n IIssnan

+ ?++@ +

A ?+A@

+ ?A+@ A

A ?AA@


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Contohpengisiantempatangtersedia

!


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con$o soa =

+a"%#a -an T"o: #n-a .#aan#n#"an/an -a"% AS .#n As$"a%a .#a%(#s%" a$a In-%a

Da"% AS # (#s%" a-a 1 a" #n#"an/an -an-a"% (#s%" # As$"a%a a-a 2 a" #n#"an/an

Da"% AS # In-%a a-a 3 a" #n#"an/an -an-a"% In-%a # As$"a%a a-an 2 a" #n#"an/an

T%-a a-a #n#"an/an -a"% (#s%" # In-%a

B#"aa an:a a" #n#"an/an :an/ -aa$-%$#. n$ ##"/%an -a"% AS # As$"a%a

L%a$ %s$"as% -% s%-##"%$n:a


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sos% =

Ban:a ca"a ##"/%an -a"% AS#As$"a%a.#a%(#s%"=

Da"% AS # (#s%" -aa$ -%%% 1 a"

#n#"an/anDa"% (#s%" # As$"a%a -aa$ -%%% 2

a" #n#"an/an

Da"% AS # As$"a%a ?.#a% (#s%"@-aa$ -%%% 1 X 2 2 a"#n#"an/an


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Ban:a ca"a ##"/%an -a"% AS#As$"a%a.#a%In-%a=

Da"% AS # In-%a -aa$ -%%% 3 a"#n#"an/an

Da"% In-%a # As$"a%a -aa$ -%%% 2 a"#n#"an/an

Da"% AS # As$"a%a ?.#a% In-%a@ -aa$-%%% 3 X 2 6 a" #n#"an/an

Ca-% an:a a" :an/ -aa$ -%$#.-a"% AS # As$"a%a s#"n:a a-a 2 68 a"


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"a#torial $%&

n! n ?n1@ ?n2@ ?n3@ 1

n an//o$a -a"% %an/an a$

?n F %an/an a$ @


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Permutasi $P&

n an:a ns" :an/ $#"s#-%a" an:a ns" :an/ -%a.%

nP" n !

?n G " @ !


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con$o soa =

'o/


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sos% =

Ban:a ssnan o"/an%sas% :an/ -aa$ -%#n$ =

8P3

8 !

?8 G 3@ !

8 X 7 H 6 H 5 !

5 !

336 ssnan


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Permutasi ang 'emuat

Unsur ang Sama

n an:an:a .a ns"

. an:an:a ns" :an/ sa.a

nP" n !

! ! ( !


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con$o soa =

B#"aa an:a ssnan ":an/ -aa$ -%ssn -a"% "

" -aa. a$a (A+IIAN


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sos% =

Ban:a " -aa. a$a (A+IIAN 8

Ban:a " :an/ sa.a 2 ?" A@ -an 2 ?" I@

P 8 !

2 ! 2 !

8 X 7 H 6 H 5 H 4 H 3 H 2 !

2 H 1 H 2 !

10080 ssnan "


41/85

Permutasi Si#lis

Ps%16%s?n1@!

n an:an:a ns" :an/ $#"s#-%a


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con$o soa =

T"o: +a"%#a a- Ta:o" R:an-an Sa"a: aan .#n/a-aan "aa$$#"$$ -% sa$ .#a :an/

#"#n$ %n/a"an B#"aa an:assnan $#.a$ -- :an/ .n/%n$#"a-%


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sos% =

Ssnan $#.a$ -- :an/ .n/%n$#"a-% =

Ps%16%s ?61@! 5!

5 H 4 H 3 H 2 H 1120


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*o.%nas% ?@

n an:an:a ns" :an/ $#"s#-%a" an:an:a ns" :an/ -%a.%

n"

n !

?n G " @ ! " !


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con$o soa =

Da"% 11 no# :an/ $#"-%"% -a"%7 no# 'a"": Po$$#"-an4 no# T


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sos% =

3 no# 'a"": Po$$#" -%%% -a"% 7 no#:an/ $#"s#-%a =

73 7 !

?7 G 3@ ! 3 !

7 H 6 H 5 H 4 !

4 ! H 3 H 2 H 1

35 ssnan


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2 no# T


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Ca-% an:a #.n/%nan

$#"%%n:a 3 no# 'a"": Po$$#" -an2 no# T


50/85

Segitiga Pascal

?a@2a2 2a 2

?a@4a4 4a3 6a22 4a3 4

(

( 2 (

( ) ) (

( * + * (

( , (- (- , (


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Segitiga Pascal $dengan #ombinasi&

C C

C C C

C C C C

C C C C C

0

1 1

1

1

1

1

0

0

0

2 2 22

2

2

3

3 3 3

3

3

4 4 4 4 4

4


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Pen.abaran /inom Ne0ton

?a@n an5% %

% s 1

n

%o

n

%


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con$o soa =

T#n$an o#Js%#n s :an/

.#.a$ H:2

a-a #naa"an ?2H :@3!


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sos% =

?2H :@3

a 2H

:

n 3

% 2

an% %

?2H@32:2

6H:2

n%

3

2


55/85

Peluang Suatu Ke.adian

0 K P?A@ K 1

P?A@ #an/ #a-%an A

n?A@ an:a an//o$a %.nan #a-%an A

n?S@ an:a an//o$a %.nan s#.a#a-%an #.n/%nan "an/ sa.#

"an/ con$o

P?A@ n?A@

n?S@


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con$o soa =

Da"% s##"an/a$ a"$ "#.% ?$ana

o#"@ #"aaa #an/ $#"a.%n:aa"$ As


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sos% =

P#an/ $#"a.%n:a a"$ As =

P?As@ n?As@

n?S@

4

52

1

13


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"re#uensi 1arapan Suatu Ke.adian

M?A@ n H P?A@

M?A@ "##ns% a"aan #a-%an A

n an:an:a #"coaan

P?A@ #an/ #a-%an A


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Da -a- -%#.a" #"sa.aans#an:a 36 a% T#n$an "##ns%

a"aan .ncn:a -a .a$a -a-#.a 11 a$a 12 !

con$o soa =


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SOLSI =

(%saan E #a-%an .ncn:a -a.a$a -a- #".a 11 a$a 12 .aa E

?56@ ?65@ ?66@ Q n ?E@ 3

P?E@ n?E@

3

1

n?S@ 36 12

M?E@ N H P ?E@ 36 H1

312


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Peluang Komplemen suatu #e.adian

P ?A@ 1 P?A@

P?A@ #an/ #a-%an A

P?A@ #an/ #a-%an s#a%n A


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con$o soa =

Da a o%n -%#.a" #"sa.asa.a #an/ .ncn:a s%s% /a.a"

a-aa 04 B#"aa #an/.ncn:a s%s% an/a


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SOLSI =

P ?/a.a"@ 04

P ?an/a@ 1 G P ?/a.a"@1 G 04

06


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Peluang Ke.adian 'a.emu#

P?AB@ P?A@ P?B@ G P?AB@

P?A@ #an/ #a-%an A

P?B@ #an/ #a-%an B

P?AB@ #an/ #a-%an A a$a #a-%an BP?AB@ #an/ #a-%an A -an #a-%an B


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iagram 3enn Peluang Ke.adian 'a.emu#

A B


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con$o soa =

2 a -a- -%#.a" s#ca"a#"sa.aan '%$n/ #an/

.ncn:a .a$a -a- #"$a.a #%-a"% 5 a$a .a$a -a- #-a#%a$an 3 !


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SOLSI =

A{?61@?62@?63@?64@?65@?66@}

B{?13@?16@?23@?26@?33@?36@?43@?46@ ?53@?56@?63@?66@}

P?AB@{?63@?66@}

P?AB@ P?A@ P?B@ G P?AB@

6

12

2

36 36 36

16

4

36 9


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Peluang Ke.adian Saling 4epas

P?AB@ P?A@ P?B@

A -an B #a-%an sa%n/ #as ? $%-a$#"a-% s#ca"a #"sa.aan@

P?A@ #an/ #a-%an A

P?B@ #an/ #a-%an BP?AB@ #an/ #a-%an A a$a #a-%an B


69/85

iagram 3enn Peluang Ke.adian Saling 4epas

A B


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con$o soa =

2 a -a- -%#.a" 1 a% s#ca"a#"sa.aan '%$n/a #an/

.ncn:a .a #-a .a$a -a- 2a$a 5


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SOLSI =

n?S@ 36

A a-aa #"%s$%


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P?AB@ P?A@ P?B@

n?A@

n?B@

n?S@ n?S@

1

4

36 36

5

36


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Peluang Ke.adian Saling bebas

P?AB@ P?A@ H P?B@

A -an B #a-%an sa%n/ #as ?$%-asa%n/ .#.#n/a"%


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con$o soa =

Sa$ a -a- -an sa$ a an/o/a. -%#.a" #"sa.aan

B#"aaa #an/ .ncn:a.a$a -a- 2 -an s%s% /a.a" a-aan/ o/a.


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SOLSI =

P ?A@ #an/ .ncn:a .a$a -a- 2P ?B@ #an/ .ncn:a s%s% /a.a" a-a an/

o/a.

P?B@

1

2P?A@

1

6

P?AB@ P?A@ X P?B@

1

X

1

6 2

1

12


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Peluang Ke.adian /ersarat

P#an/ #a-%an A -#n/an s:a"a$ #a-%an B $#"a-% #% -a-%$#n$an -#n/an a$"an =

P#an/ #a-%an B -#n/an s:a"a$ #a-%an A $#"a-% #% -a-%$#n$an -#n/an a$"an =

P?AB@ P?AB@P?AB@ P?AB@

P?A|B@

P?AB@

P?B@

P?B|A@

P?AB@

P?A@


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con$o soa =

*#a-%an A .#.n:a% #an/ P?A@15 -an #a-%an B .#.n:a%#an/ P ?B@ 12 B#"aaa P?A|B@


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SOLSI =

P ?A|B@ P ?AB@

P?B@

110

12

15


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T'E END


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DIRETED BY

ARIO ARI&ANDANA 'ALI(


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SLIDEPLAY BY

EL)IN (AR&ADY


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PRODER

*ARINA D&IYANI +A,ALI


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DIRETOR OM ANI(ATION

STE)EN TANI*O


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EDITED BY

NIA TANIA


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co:"%/$ 2009

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