Teoria Probabilidad 17 18 Teleco - CECyT 3 Estanislao ... · ,1'(3(1'(1&,$ 3$5$ 75(6 2 0È6 68&(626...

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7(0$ 352%$%,/,'$' &8562 ,QWURGXFFLyQ 'HILQLFLyQ D[LRPiWLFD GH SUREDELOLGDG &RQVHFXHQFLDV GH ORV D[LRPDV &RPELQDWRULD 5HJOD GHO SURGXFWR 3UREDELOLGDG FRQGLFLRQDGD ,QGHSHQGHQFLD GH VXFHVRV 7HRUHPDV GH OD 3UREDELOLGDG 7RWDO \ GH %D\HV Autor : Teoría de la Probabilidad 1718por Teleco Material recopilado en internet para I.P.N. por I.Q. Rafael Arturo Granados Jiménez

Transcript of Teoria Probabilidad 17 18 Teleco - CECyT 3 Estanislao ... · ,1'(3(1'(1&,$ 3$5$ 75(6 2 0È6 68&(626...

Page 1: Teoria Probabilidad 17 18 Teleco - CECyT 3 Estanislao ... · ,1'(3(1'(1&,$ 3$5$ 75(6 2 0È6 68&(626 'hilqlflyq 6hdq a !a n vxfhvrv fxdohvtxlhud vh glfh txh vrq vxfhvrv lqghshqglhqwhv

Autor  :  Teoría  de  la  Probabilidad  17-­18-­por  Teleco

Material  recopilado  en  internet  para  I.P.N.  por  I.Q.  Rafael  Arturo  Granados  Jiménez

Page 2: Teoria Probabilidad 17 18 Teleco - CECyT 3 Estanislao ... · ,1'(3(1'(1&,$ 3$5$ 75(6 2 0È6 68&(626 'hilqlflyq 6hdq a !a n vxfhvrv fxdohvtxlhud vh glfh txh vrq vxfhvrv lqghshqglhqwhv
Page 3: Teoria Probabilidad 17 18 Teleco - CECyT 3 Estanislao ... · ,1'(3(1'(1&,$ 3$5$ 75(6 2 0È6 68&(626 'hilqlflyq 6hdq a !a n vxfhvrv fxdohvtxlhud vh glfh txh vrq vxfhvrv lqghshqglhqwhv
Page 4: Teoria Probabilidad 17 18 Teleco - CECyT 3 Estanislao ... · ,1'(3(1'(1&,$ 3$5$ 75(6 2 0È6 68&(626 'hilqlflyq 6hdq a !a n vxfhvrv fxdohvtxlhud vh glfh txh vrq vxfhvrv lqghshqglhqwhv

S

S

Page 5: Teoria Probabilidad 17 18 Teleco - CECyT 3 Estanislao ... · ,1'(3(1'(1&,$ 3$5$ 75(6 2 0È6 68&(626 'hilqlflyq 6hdq a !a n vxfhvrv fxdohvtxlhud vh glfh txh vrq vxfhvrv lqghshqglhqwhv

A B

A B A BA B

A B A BA B A

B A BA

A AA B A-B

A B A B A BA B, A B

A B

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A B B AA B B A A A A

A B C A B C

A B C A B C

A A A A A A

A B C A B A C

A B C A B A C

A A A A

A B A BA B A B

A A A

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Page 8: Teoria Probabilidad 17 18 Teleco - CECyT 3 Estanislao ... · ,1'(3(1'(1&,$ 3$5$ 75(6 2 0È6 68&(626 'hilqlflyq 6hdq a !a n vxfhvrv fxdohvtxlhud vh glfh txh vrq vxfhvrv lqghshqglhqwhv

S

P S

P

i i IA

i jA A i j

i ii Ii I

P A P A

IS P

Page 9: Teoria Probabilidad 17 18 Teleco - CECyT 3 Estanislao ... · ,1'(3(1'(1&,$ 3$5$ 75(6 2 0È6 68&(626 'hilqlflyq 6hdq a !a n vxfhvrv fxdohvtxlhud vh glfh txh vrq vxfhvrv lqghshqglhqwhv

A

A P A

P A P A P A P A

P

AP A P A B P A B

BP A B P A B P A P A B

Page 10: Teoria Probabilidad 17 18 Teleco - CECyT 3 Estanislao ... · ,1'(3(1'(1&,$ 3$5$ 75(6 2 0È6 68&(626 'hilqlflyq 6hdq a !a n vxfhvrv fxdohvtxlhud vh glfh txh vrq vxfhvrv lqghshqglhqwhv

A B A B

o P A P B

o P B A P B P A

A BP A B P A P B P A B

A B C

P A B C P A P B P C

P A B P A C P B C P A B C

n n nn

n i i j i j k ni i j i j k

P A A A P A P A A P A A A P A A A

Page 11: Teoria Probabilidad 17 18 Teleco - CECyT 3 Estanislao ... · ,1'(3(1'(1&,$ 3$5$ 75(6 2 0È6 68&(626 'hilqlflyq 6hdq a !a n vxfhvrv fxdohvtxlhud vh glfh txh vrq vxfhvrv lqghshqglhqwhv

nA A A

iA i n

B B

j

jA B

P B P A

iA i n

k n B BP Bn n

B

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n kV

n n n k

kn kVR n

n k

n nCk k n k

nP nr

nk k k

r

r

nPRk k k

k k k n

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kn n n

Page 14: Teoria Probabilidad 17 18 Teleco - CECyT 3 Estanislao ... · ,1'(3(1'(1&,$ 3$5$ 75(6 2 0È6 68&(626 'hilqlflyq 6hdq a !a n vxfhvrv fxdohvtxlhud vh glfh txh vrq vxfhvrv lqghshqglhqwhv
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A B

P A P B

P B A P B A

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A B BA B AP B A P A

P B AP B A

P A

P B A

P A P A B

P B A

Page 17: Teoria Probabilidad 17 18 Teleco - CECyT 3 Estanislao ... · ,1'(3(1'(1&,$ 3$5$ 75(6 2 0È6 68&(626 'hilqlflyq 6hdq a !a n vxfhvrv fxdohvtxlhud vh glfh txh vrq vxfhvrv lqghshqglhqwhv

P A B P A B

P A B C P A C P B C A B

P B A P A P B A

P A P B A

P A B C P A P B A P C A B

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n n nP A A A P A P A A P A A A P A A A A

P A B P B A

P A B P A BP A B P B A

P B P A

a P A B P A B P B P B A P A

P B P A Bb P B A

P A

Page 19: Teoria Probabilidad 17 18 Teleco - CECyT 3 Estanislao ... · ,1'(3(1'(1&,$ 3$5$ 75(6 2 0È6 68&(626 'hilqlflyq 6hdq a !a n vxfhvrv fxdohvtxlhud vh glfh txh vrq vxfhvrv lqghshqglhqwhv

P B A P B

P B A P A B

Page 20: Teoria Probabilidad 17 18 Teleco - CECyT 3 Estanislao ... · ,1'(3(1'(1&,$ 3$5$ 75(6 2 0È6 68&(626 'hilqlflyq 6hdq a !a n vxfhvrv fxdohvtxlhud vh glfh txh vrq vxfhvrv lqghshqglhqwhv

B C

P B C P B

B C

A B A B

P A B P A P B A P B

A B

Page 21: Teoria Probabilidad 17 18 Teleco - CECyT 3 Estanislao ... · ,1'(3(1'(1&,$ 3$5$ 75(6 2 0È6 68&(626 'hilqlflyq 6hdq a !a n vxfhvrv fxdohvtxlhud vh glfh txh vrq vxfhvrv lqghshqglhqwhv

A B

A B P A B P A P B

P A B

P A P B

Page 22: Teoria Probabilidad 17 18 Teleco - CECyT 3 Estanislao ... · ,1'(3(1'(1&,$ 3$5$ 75(6 2 0È6 68&(626 'hilqlflyq 6hdq a !a n vxfhvrv fxdohvtxlhud vh glfh txh vrq vxfhvrv lqghshqglhqwhv

A B

A B A B

Page 23: Teoria Probabilidad 17 18 Teleco - CECyT 3 Estanislao ... · ,1'(3(1'(1&,$ 3$5$ 75(6 2 0È6 68&(626 'hilqlflyq 6hdq a !a n vxfhvrv fxdohvtxlhud vh glfh txh vrq vxfhvrv lqghshqglhqwhv

nA A

ki iA A

nA A

k ki i i iP A A P A P A

P A B P A P B

P A C P A P C

P B C P B P C

P A B C P A P B P C

Page 24: Teoria Probabilidad 17 18 Teleco - CECyT 3 Estanislao ... · ,1'(3(1'(1&,$ 3$5$ 75(6 2 0È6 68&(626 'hilqlflyq 6hdq a !a n vxfhvrv fxdohvtxlhud vh glfh txh vrq vxfhvrv lqghshqglhqwhv
Page 25: Teoria Probabilidad 17 18 Teleco - CECyT 3 Estanislao ... · ,1'(3(1'(1&,$ 3$5$ 75(6 2 0È6 68&(626 'hilqlflyq 6hdq a !a n vxfhvrv fxdohvtxlhud vh glfh txh vrq vxfhvrv lqghshqglhqwhv

P A B C P A P B A P C A B

n

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nA A A

n

ii

A

i jA A i j i j nB S

n

i ii

P B P A P B A

jA j n

j jj n

i ii

P A P B AP A B

P A P B A

Page 27: Teoria Probabilidad 17 18 Teleco - CECyT 3 Estanislao ... · ,1'(3(1'(1&,$ 3$5$ 75(6 2 0È6 68&(626 'hilqlflyq 6hdq a !a n vxfhvrv fxdohvtxlhud vh glfh txh vrq vxfhvrv lqghshqglhqwhv

Ai iP A P S A P B

A

Page 28: Teoria Probabilidad 17 18 Teleco - CECyT 3 Estanislao ... · ,1'(3(1'(1&,$ 3$5$ 75(6 2 0È6 68&(626 'hilqlflyq 6hdq a !a n vxfhvrv fxdohvtxlhud vh glfh txh vrq vxfhvrv lqghshqglhqwhv

P A

ki i

j jkj

j jj

P A B P A P B AP B P B

P A B P A P B A P B P A P B AP A P B A

A B C P C

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P A P B A P B P A B

P A B P A P B A B

A B C P C

n

n n

P A A AP A P A P A A A A