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3Opción B

2 puntos

Elija solo uno de los apartados A) o B):

Sean AA y BB dos sucesos del espacio muestral asociado a un experimento aleatorio. Se sabe que P(A)P(A) es el doble de P(B)P(B), P(Bc/A)=0,75P(B^c/A)=0{,}75 y P(A∩B)=0,2P(A\cap B)=0{,}2.
a
Calcule la probabilidad de que ocurra BB.0,5 pts
b
Calcule la probabilidad de que no ocurra ni AA ni BB. ¿Son los sucesos AcA^c y BcB^c incompatibles?0,5 pts
c
Si el experimento se realiza 13501350 veces de forma independiente:
i
Determine la distribución de la variable aleatoria XX: "Número de veces que ocurre BB".0,25 pts
ii
Calcule la probabilidad de que BB ocurra a lo sumo 580580 veces, pero más de 499499 veces.0,75 pts

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FUNCIÓN DE DISTRIBUCIÓN NORMAL N(0,1)N(0,1)
Distribución normal N(0, 1), con el área de probabilidad hasta z sombreada, el eje vertical en 0 y las marcas menos infinito, 0, z y más infinito.
zz0,000,010,02
0,00,50000,50400,5080
0,10,53980,54380,5478
0,20,57930,58320,5871
0,30,61790,62170,6255
0,40,65540,65910,6628
0,50,69150,69500,6985
0,60,72570,72910,7324
0,70,75800,76110,7642
0,80,78810,79100,7939
0,90,81590,81860,8212
1,00,84130,84380,8461
1,10,86430,86650,8686
1,20,88490,88690,8888
1,30,90320,90490,9066
1,40,91920,92070,9222
1,50,93320,93450,9357
1,60,94520,94630,9474
1,70,95540,95640,9573
1,80,96410,96490,9656
1,90,97130,97190,9726
2,00,97720,97780,9783
2,10,98210,98260,9830
2,20,98610,98640,9868
2,30,98930,98960,9898
2,40,99180,99200,9922
2,50,99380,99400,9941
2,60,99530,99550,9956
2,70,996530,996640,99674
2,80,997440,997520,99760
2,90,998130,998190,99825
3,00,998650,998690,99874
3,10,999030,999060,99910
3,20,999310,999340,99936
3,30,999520,999530,99955
3,40,999660,999680,99969
3,50,999770,999780,99978
3,60,999840,999850,99985
3,70,999890,999900,99990
3,80,999930,999930,99993
3,90,999950,999950,99996
4,00,999970,999970,99997
zz0,030,040,05
0,00,51200,51600,5199
0,10,55170,55570,5596
0,20,59100,59480,5987
0,30,62930,63310,6368
0,40,66640,67000,6736
0,50,70190,70540,7088
0,60,73570,73890,7422
0,70,76730,77040,7734
0,80,79670,79950,8023
0,90,82380,82640,8289
1,00,84850,85080,8531
1,10,87080,87290,8749
1,20,89070,89250,8944
1,30,90820,90990,9115
1,40,92360,92510,9265
1,50,93700,93820,9394
1,60,94840,94950,9505
1,70,95820,95910,9599
1,80,96640,96710,9678
1,90,97320,97380,9744
2,00,97880,97930,9798
2,10,98340,98380,9842
2,20,98710,98750,9878
2,30,99010,99040,9906
2,40,99250,99270,9929
2,50,99430,99450,9946
2,60,99570,99590,9960
2,70,996830,996930,99702
2,80,997670,997740,99781
2,90,998310,998360,99841
3,00,998780,998820,99886
3,10,999130,999160,99918
3,20,999380,999400,99942
3,30,999570,999580,99960
3,40,999700,999710,99972
3,50,999790,999800,99981
3,60,999860,999860,99987
3,70,999900,999910,99991
3,80,999940,999940,99994
3,90,999960,999960,99996
4,00,999970,999970,99997
zz0,060,070,08
0,00,52390,52790,5319
0,10,56360,56750,5714
0,20,60260,60640,6103
0,30,64060,64430,6480
0,40,67720,68080,6844
0,50,71230,71570,7190
0,60,74540,74860,7517
0,70,77640,77940,7823
0,80,80510,80780,8106
0,90,83150,83400,8365
1,00,85540,85770,8599
1,10,87700,87900,8810
1,20,89620,89800,8997
1,30,91310,91470,9162
1,40,92790,92920,9306
1,50,94060,94180,9429
1,60,95150,95250,9535
1,70,96080,96160,9625
1,80,96860,96930,9699
1,90,97500,97560,9761
2,00,98030,98080,9812
2,10,98460,98500,9854
2,20,98810,98840,9887
2,30,99090,99110,9913
2,40,99310,99320,9934
2,50,99480,99490,9951
2,60,99610,99620,9963
2,70,997110,997200,99728
2,80,997880,997950,99801
2,90,998460,998510,99856
3,00,998890,998930,99896
3,10,999210,999240,99926
3,20,999440,999460,99948
3,30,999610,999620,99964
3,40,999730,999740,99975
3,50,999810,999820,99983
3,60,999870,999880,99988
3,70,999920,999920,99992
3,80,999940,999950,99995
3,90,999960,999960,99997
4,00,999980,999980,99998
zz0,09
0,00,5359
0,10,5753
0,20,6141
0,30,6517
0,40,6879
0,50,7224
0,60,7549
0,70,7852
0,80,8133
0,90,8389
1,00,8621
1,10,8830
1,20,9015
1,30,9177
1,40,9319
1,50,9441
1,60,9545
1,70,9633
1,80,9706
1,90,9767
2,00,9817
2,10,9857
2,20,9890
2,30,9916
2,40,9936
2,50,9952
2,60,9964
2,70,99736
2,80,99807
2,90,99861
3,00,99900
3,10,99929
3,20,99950
3,30,99965
3,40,99976
3,50,99983
3,60,99989
3,70,99992
3,80,99995
3,90,99997
4,00,99998
Nota: En el interior de la tabla se da la probabilidad de que la variable aleatoria ZZ, con distribución N(0,1)N(0,1), esté por debajo del valor zz.