regla general y particular de la multiplicaciÓn de probabilidades
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5/9/2018 REGLA GENERAL Y PARTICULAR DE LA MULTIPLICACI N DE PROBABILIDADES - slidepdf.com
http://slidepdf.com/reader/full/regla-general-y-particular-de-la-multiplicacion-de-probabilid
PLFAC FLHLPCA _ TCPZOB\ACP JL AC N\AZOTAOBCBOÒH JLTPI@C@OAOJCJLR
3/ PLFAC FLHLPCA TCPC LULHZIR JLTLHJOLHZLR
Ro C y @ rih jir lulhzir jltlhjolhzlr! lr jlbop! ro ac ib|pplhboc jl C celbzc ac tpi`c`oaojcjjl ib|pplhboc jl @! lhzihblr! jobmc tpi`c`oaojcj jl bcab|ac lntalchji ac rof|olhzl plfac;
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Lh jihjl;
La bihlbzoui ‑ y„ bipplrtihjl c ac ‑ohzlprlbboòh„ lh ac zlipîc jl bihk|hzir -y >/La lrtcboi n|lrzpca -R/ bipplrtihjl ca bihk|hzi |houlpri lh ac zlipîc jl bihk|hzir
-/
Hizc; Ac tpi`c`oaojcj jla lulhzi @! bcab|acjc `cki ac r|tiroboòh jl s|l la lulhzi C mc ib|ppoji!
rl jlhinohc tpi`c`oaojcj bihjoboihca jl @! jcji C! y rl jlhizc tip T -@)C/(Ro rl jlrlc i`zlhlp |hc eòpn|ac tcpc bcab|acp ac tpi`c`oaojcj bihjoboihca rl jlrtlkc jl ac
eòpn|ac flhlpca jl ac n|azotaobcboòh- / - / -/! i`zlhoïhjirl;
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Ac tpi`c`oaojcj bihjoboihca jl C jcji @ rl jlhizc tip T-C)@/ y rl bcab|ac lntalchji acrof|olhzl eòpn|ac;
-/ - /
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Lklntair oa|rzpczouir
3/ Jl |hc `cpckc lrzãhjcp jl <0 bcpzcr rlc C la r|blri jl rcbcp |h Cr lh ac tponlpc
l}zpcbboòh y @ rcbcp |h Cr lh ac rlf|hjc l}zpcbboòh( Bcab|acp ac tpi`c`oaojcj jl rcbcp jirCrlr lh jir l}zpcbboihlr roh jluiaulp ac bcpzc l}zpcîjc(
Ria|boòh;
5/9/2018 REGLA GENERAL Y PARTICULAR DE LA MULTIPLICACI N DE PROBABILIDADES - slidepdf.com
http://slidepdf.com/reader/full/regla-general-y-particular-de-la-multiplicacion-de-probabilid
C y @ rih r|blrir jltlhjolhzlr tips|l ac ib|pplhboc jl C celbzc ac tpi`c`oaojcj jl
ib|pplhboc jl @(
Ac tpi`c`oaojcj jl s|l ac tponlpc bcpzc rlc |h Cr lr;
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Ac tpi`c`oaojcj jl s|l ac rlf|hjc bcpzc rlc |h Cr! jcji s|l yc rl rcbò |h Cr lh ac tponlpc
l}zpcbboòh! lr;
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Pllntac{chji air chzlpoiplr ucaiplr lh ac plfac flhlpca jl ac n|azotaobcboòh jl
tpi`c`oaojcjlr tcpc lulhzir jltlhjolhzlr rl i`zolhl;
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0/ Rlc C la r|blri jl rcbcp |h Cr jl |hc `cpckc lrzãhjcp jl <0 bcpzcr y @ rcbcp |h Ply jlbipc{òh piki( Bcab|acp ac tpi`c`oaojcj jl rcbcp |h Cr y |h Ply jl bipc{òh piki lh jir
l}zpcbboihlr roh jluiaulp ac bcpzc l}zpcîjc(
Ria|boòh;
C y @ rih r|blrir jltlhjolhzlr tips|l ac ib|pplhboc jl C celbzc ac tpi`c`oaojcj jl
ib|pplhboc jl @(
Ac tpi`c`oaojcj jl s|l ac tponlpc bcpzc rlc |h Cr lr;
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Ac tpi`c`oaojcj jl s|l ac rlf|hjc bcpzc rlc |h Ply! jcji s|l yc rl rcbò |h Cr lh ac
tponlpc l}zpcbboòh lr;
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Pllntac{chji air chzlpoiplr ucaiplr lh ac plfac flhlpca jl ac n|azotaobcboòh jl
tpi`c`oaojcjlr tcpc lulhzir jltlhjolhzlr rl i`zolhl;
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5/9/2018 REGLA GENERAL Y PARTICULAR DE LA MULTIPLICACI N DE PROBABILIDADES - slidepdf.com
http://slidepdf.com/reader/full/regla-general-y-particular-de-la-multiplicacion-de-probabilid
2/ Lh |hc bacrl jl <4 ca|nhir! 34 ca|nhir zolhlh bini tplelplhboc riacnlhzl accrofhcz|pc jl Nczlnãzobc! 3< tpleolplh riacnlhzl Lrzcjîrzobc y < hi zolhlh tplelplhboc tip
hohf|hc jl lrzcr crofhcz|pcr( Bcab|acp ac tpi`c`oaojcj s|l jl |h ca|nhi jl ac bacrl
rlalbboihcji ca c{cp zlhfc tplelplhboc tip
:(3/ Nczlnãzobc y Lrzcjîrzobc(
:(0/ Lrzcjîrzobc y Nczlnãzobc
Ria|boòh;Plcao{chji |h jocfpcnc jl Ulhh.L|alp rl i`zolhl;
Ron`iaifîc;
R > lrtcboi n|lrzpcaC> Nczlnãzobc
@ > Lrzcjîrzobc
c > Riacnlhzl Nczlnãzobc
` > Riacnlhzl Lrzcjîrzobcb > Nczlnãzobc y Lrzcjîrzobc
j > Hohf|hc jl acr jir crofhcz|pcr
Jczir y bãab|air;
c > 34
` > 3<
b > R ‒ c ‒ ` ‒ j > <4 ‒ 34 ‒ 3< ‒ < > 04j > <
R > <4
:(3/ Nczlnãzobc y Lrzcjîrzobc(
-/
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Lhzihblr! ctaobchji ac eòpn|ac jl ac tpi`c`oaojcj zlòpobc rl i`zolhl;
-/
-/
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5/9/2018 REGLA GENERAL Y PARTICULAR DE LA MULTIPLICACI N DE PROBABILIDADES - slidepdf.com
http://slidepdf.com/reader/full/regla-general-y-particular-de-la-multiplicacion-de-probabilid
I zcn`oïh! i`rlpuchji la jocfpcnc jl Ulhh.L|alp rl zolhl joplbzcnlhzl ac tpi`c`oaojcjriaobozcjc;
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Tcpc ctaobcp ac plfac jl ac n|azotaobcboòh tcpc lulhzir jltlhjolhzlr! i`rlpuchji la
jocfpcnc jl Ulhh.L|alp rl zolhl;
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Ac r|tiroboòh jl s|l la ca|nhi rlalbboihcji zlhfc tplelplhboc tip Nczlnãzobc rofhoeobc
s|l ròai bihrojlplnir la bihk|hzi C! jl air 24 lalnlhzir jl C! ròai 04 zolhlh tplelplhboctip Lrzcjîrzobc( Tip ai zchzi ac tpi`c`oaojcj bihjoboihca T-@)C/ > 04)24 > 0)2
I zcn`oïh! i`rlpuchji la jocfpcnc jl Ulhh.L|alp y ctaobchji ac eòpn|ac jl actpi`c`oaojcj bihjoboihca rl zolhl;
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Pllntac{chji ucaiplr lh ac plfac jl ac n|azotaobcboòh tcpc lulhzir jltlhjolhzlr rl
i`zolhl;
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- /
:(0/ Lrzcjîrzobc y Nczlnãzobc(
-/
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Lhzihblr! ctaobchji ac eòpn|ac jl ac tpi`c`oaojcj zlòpobc rl i`zolhl;
-/
-/
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5/9/2018 REGLA GENERAL Y PARTICULAR DE LA MULTIPLICACI N DE PROBABILIDADES - slidepdf.com
http://slidepdf.com/reader/full/regla-general-y-particular-de-la-multiplicacion-de-probabilid
I zcn`oïh i`rlpuchji la jocfpcnc jl Ulhh.L|alp rl zolhl joplbzcnlhzl ac tpi`c`oaojcj
riaobozcjc;
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Tcpc ctaobcp ac plfac jl ac n|azotaobcboòh tcpc lulhzir jltlhjolhzlr! i`rlpuchji la
jocfpcnc jl Ulhh.L|alp rl zolhl;
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Ac r|tiroboòh jl s|l la ca|nhi rlalbboihcji zlhfc tplelplhboc tip Lrzcjîrzobc rofhoeobc s|lròai bihrojlplnir la bihk|hzi @! jl air 2< lalnlhzir jl @! ròai 04 zolhlh tplelplhboc tip
Nczlnãzobc( Tip ai zchzi ac tpi`c`oaojcj bihjoboihca T-C)@/ > 04)2< > :)6
Pllntac{chji ucaiplr lh ac plfac flhlpca jl ac n|azotaobcboòh;
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Air bãab|air lh L}bla rl n|lrzpch lh ac rof|olhzl eof|pc;
Hizcr;Lh air lulhzir jltlhjolhzlr rl b|ntal;
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5/9/2018 REGLA GENERAL Y PARTICULAR DE LA MULTIPLICACI N DE PROBABILIDADES - slidepdf.com
http://slidepdf.com/reader/full/regla-general-y-particular-de-la-multiplicacion-de-probabilid
La plr|azcji jl - / - /! roh ln`cpfi! la tpiblri jl bãab|ai lr joelplhzl(
:/ Jl |hc zòn`iac s|l bihzolhl 2 `iacr pikcr y < `achbcr! Nczmîcr l}zpcl zplr `iacr! roh
uiaulp c ac zòn`iac ac `iac l}zpcîjc! bcab|acp ac tpi`c`oaojcj jl s|l acr 2 `iacr l}zpcîjcr
rlch;
5(3/ Pikcr5(0/ 0 pikcr y |hc `achbc
5(2/ \hc pikc y 0 `achbcr5(:/ 2 `achbcr
Ria|boòh;
5(3/ Pikcr
Lh 2 r|blrir ac eòpn|ac jl ac plfac flhlpca jl tpi`c`oaojcjlr lr;
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Ac tpi`c`oaojcj jl rlalbboihcp |hc `iac pikc ac tponlpc l}zpcbboòh lr;
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Ac tpi`c`oaojcj jl rlalbboihcp |hc `iac pikc ac rlf|hjc l}zpcbboòh! jcji s|l yc rlrlalbboihò |hc `iac pikc lh ac tponlpc l}zpcbboòh lr;
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Ac tpi`c`oaojcj jl rlalbboihcp |hc `iac pikc ac zlpblpc l}zpcbboòh! jcji s|l yc rl
rlalbboihò |hc `iac pikc lh ac tponlpc y lh ac rlf|hjc l}zpcbboòh lr;
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Pllntac{chji ucaiplr lh ac plfac flhlpca jl jl ac n|azotaobcboòh rl i`zolhl;
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5/9/2018 REGLA GENERAL Y PARTICULAR DE LA MULTIPLICACI N DE PROBABILIDADES - slidepdf.com
http://slidepdf.com/reader/full/regla-general-y-particular-de-la-multiplicacion-de-probabilid
I zcn`oïh! lac`ipchji |h jocfpcnc jl ãp`ia rl zolhl zijcr acr tpi`c`oaojcjlr;
Lh la jocfpcnc jl ãp`ia! ac tpi`c`oaojcj bipplrtihjolhzl c bcjc pcnc jla ãp`ia bipplrtihjl
c ac tpi`c`oaojcj bihjoboihca jl s|l ib|ppc la lulhzi lrtlbîeobi! jcji s|l mch ib|ppoji airlulhzir jl acr pcncr tplbljlhzlr( Ca jlrbpo`op |h lulhzi nljochzl |hc zpcylbzipoc c zpcuïr
jla jocfpcnc jl ãp`ia! ac tpi`c`oaojcj jl s|l ib|ppc jobmi lulhzi lr of|ca c tpij|bzi jl acr
tpi`c`oaojcjlr jl acr pcncr s|l eipnch ac zpcylbzipoc s|l pltplrlhzc ca nlhboihcji lulhzi(
Ac ria|boòh lntalchji la jocfpcnc jl ãp`ia tcpc -/ lr n|azotaobchji acr pcncr
PPP! lr jlbop!
-/
5(0/ 0 pikcr y |hc `achbc
Ac ria|boòh lntalchji la jocfpcnc jl ãp`ia rl i`zolhl n|azotaobchji acr pcncr PP@
-/
5(2/ \hc pikc y 0 `achbcr
Ac ria|boòh lntalchji la jocfpcnc jl ãp`ia rl i`zolhl n|azotaobchji acr pcncr P@@
-/
5(:/ 2 `achbcr
Ac ria|boòh lntalchji la jocfpcnc jl ãp`ia rl i`zolhl n|azotaobchji acr pcncr @@@
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5/9/2018 REGLA GENERAL Y PARTICULAR DE LA MULTIPLICACI N DE PROBABILIDADES - slidepdf.com
http://slidepdf.com/reader/full/regla-general-y-particular-de-la-multiplicacion-de-probabilid
Air bãab|air lh L}bla rl n|lrzpch lh ac rof|olhzl eof|pc;
0/ PLFAC TCPZOB\ACP I LRTLBOCA TCPC LULHZIR OHJLTLHJOLHZLR
Ro C y @ rih jir lulhzir ohjltlhjolhzlr! lr jlbop! ro la bihibonolhzi jl ac ohbojlhboc jl|hi jl laair hi zolhl lelbzi lh ac tpi`c`oaojcj jl ib|pplhboc jla izpi! lhzihblr! tcpc
bcab|acp ac tpi`c`oaojcj jl jobmir lulhzir rl ctaobc ac rof|olhzl plfac;
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Hizc; Jir lulhzir C y @ rih ohjltlhjolhzlr ro ac ib|pplhboc jl |hi jl laair hi celbzc ac
tpi`c`oaojcj jl ib|pplhboc jla izpi! lrzi lr! ro -/ -/
Lklntair oa|rzpczouir
3/ Jl |hc `cpckc lrzãhjcp jl <0 bcpzcr rlc C la r|blri jl rcbcp |h Cr lh ac tponlpc
l}zpcbboòh y @ rcbcp |h Ply lh ac rlf|hjc l}zpcbboòh( Bcab|acp ac tpi`c`oaojcj jl rcbcp |h
Cr y |h Ply lh jir l}zpcbboihlr jluiauolhji ac bcpzc l}zpcîjc(
Ria|boòh;
C y @ rih r|blrir ohjltlhjolhzlr tips|l ac ib|pplhboc jl C celbzc ac tpi`c`oaojcj jl
ib|pplhboc jl @(
Ac tpi`c`oaojcj jl s|l ac tponlpc bcpzc rlc |h Cr lr;
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Ac tpi`c`oaojcj jl s|l ac rlf|hjc bcpzc rlc |h Ply! jcji s|l rl jluiauoò la Cr jl ac
tponlpc l}zpcbboòh! lr;
5/9/2018 REGLA GENERAL Y PARTICULAR DE LA MULTIPLICACI N DE PROBABILIDADES - slidepdf.com
http://slidepdf.com/reader/full/regla-general-y-particular-de-la-multiplicacion-de-probabilid
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Pllntac{chji air chzlpoiplr ucaiplr lh ac plfac tcpzob|acp jl ac n|azotaobcboòh rl i`zolhl;
- / - / -/
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0/ \hc tcplkc jl lrtirir jlrlch zlhlp 2 mokir( R|tiholhji s|l acr tpi`c`oaojcjlr jl zlhlp|h hoói i |hc hoóc rih of|calr! bcab|acp ac tpi`c`oaojcj jl ï}ozi lh zlhlp min`pl lh la
tponlp hcbonolhzi! n|klp lh la rlf|hji hcbonolhzi y min`pl lh la zlpblp hcbonolhzi(
Ria|boòh;
N > n|klp
M > min`pl
Lac`ipchji |h jocfpcnc jl ãp`ia rl zolhl zijcr acr tpi`c`oaojcjlr;
Lhzihblr!
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