Tugas Mat Presentasi Peluang

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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

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    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@

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    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 "

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    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

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    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

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    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

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    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