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3

3 puntos
Apartado 3
En la fase final del campeonato de Europa de baloncesto juegan Alemania, Francia, Croacia y España. Las semifinales son: España-Alemania y Francia-Croacia. La probabilidad de que España gane a Alemania es 0,70{,}7, la de que gane a Francia es 0,250{,}25 y la de que gane a Croacia es 0,550{,}55. La probabilidad de que Francia pierda contra Croacia es 0,40{,}4. Se supone independencia entre los resultados de unos partidos y otros.
a
Calcula probabilidad de que la final sea Alemania-Croacia.0,5 pts
b
Calcula la probabilidad de que España sea campeona.1 pt
c
Si España ha sido campeona, ¿cuál es la probabilidad de que en la final haya jugado contra Francia?0,5 pts
d
El mes siguiente al campeonato, España y Croacia jugarán siete partidos. ¿Cuál es la probabilidad de que Croacia gane al menos cinco de esos partidos?1 pt

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TABLA DE LA DISTRIBUCIÓN BINOMIAL P[X=x]=(nx)px(1−p)n−xP[X=x]=\binom{n}{x}p^x(1-p)^{n-x} pp
nnxx0,010,050,100,150,200,250,301/31/30,350,400,450,490,50
200,98010,90250,81000,72250,64000,56250,49000,44440,42250,36000,30250,26010,2500
10,01980,09500,18000,25500,32000,37500,42000,44440,45500,48000,49500,49980,5000
20,00010,00250,01000,02250,04000,06250,09000,11110,12250,16000,20250,24010,2500
300,97030,85740,72900,61410,51200,42190,34300,29630,27460,21600,16640,13270,1250
10,02940,13540,24300,32510,38400,42190,44100,44440,44360,43200,40840,38230,3750
20,00030,00710,02700,05740,09600,14060,18900,22220,23890,28800,33410,36740,3750
30,00000,00010,00100,00340,00800,01560,02700,03700,04290,06400,09110,11760,1250
400,96060,81450,65610,52200,40960,31640,24010,19750,17850,12960,09150,06770,0625
10,03880,17150,29160,36850,40960,42190,41160,39510,38450,34560,29950,26000,2500
20,00060,01350,04860,09750,15360,21090,26460,29630,31050,34560,36750,37470,3750
30,00000,00050,00360,01150,02560,04690,07560,09880,11150,15360,20050,24000,2500
40,00000,00000,00010,00050,00160,00390,00810,01230,01500,02560,04100,05760,0625
500,95100,77380,59050,44370,32770,23730,16810,13170,11600,07780,05030,03450,0313
10,04800,20360,32810,39150,40960,39550,36020,32920,31240,25920,20590,16570,1563
20,00100,02140,07290,13820,20480,26370,30870,32920,33640,34560,33690,31850,3125
30,00000,00110,00810,02440,05120,08790,13230,16460,18110,23040,27570,30600,3125
40,00000,00000,00050,00220,00640,01460,02840,04120,04880,07680,11280,14700,1563
50,00000,00000,00000,00010,00030,00100,00240,00410,00530,01020,01850,02820,0313
600,94150,73510,53140,37710,26210,17800,11760,08780,07540,04670,02770,01760,0156
10,05710,23210,35430,39930,39320,35600,30250,26340,24370,18660,13590,10140,0938
20,00140,03050,09840,17620,24580,29660,32410,32920,32800,31100,27800,24360,2344
30,00000,00210,01460,04150,08190,13180,18520,21950,23550,27650,30320,31210,3125
40,00000,00010,00120,00550,01540,03300,05950,08230,09510,13820,18610,22490,2344
50,00000,00000,00010,00040,00150,00440,01020,01650,02050,03690,06090,08640,0938
60,00000,00000,00000,00000,00010,00020,00070,00140,00180,00410,00830,01380,0156
700,93210,69830,47830,32060,20970,13350,08240,05850,04900,02800,01520,00900,0078
10,06590,25730,37200,39600,36700,31150,24710,20480,18480,13060,08720,06040,0547
20,00200,04060,12400,20970,27530,31150,31770,30730,29850,26130,21400,17400,1641
30,00000,00360,02300,06170,11470,17300,22690,25610,26790,29030,29180,27860,2734
40,00000,00020,00260,01090,02870,05770,09720,12800,14420,19350,23880,26760,2734
50,00000,00000,00020,00120,00430,01150,02500,03840,04660,07740,11720,15430,1641
60,00000,00000,00000,00010,00040,00130,00360,00640,00840,01720,03200,04940,0547
70,00000,00000,00000,00000,00000,00010,00020,00050,00060,00160,00370,00680,0078
800,92270,66340,43050,27250,16780,10010,05760,03900,03190,01680,00840,00460,0039
10,07460,27930,38260,38470,33550,26700,19770,15610,13730,08960,05480,03520,0313
20,00260,05150,14880,23760,29360,31150,29650,27310,25870,20900,15690,11830,1094
30,00010,00540,03310,08390,14680,20760,25410,27310,27860,27870,25680,22730,2188
40,00000,00040,00460,01850,04590,08650,13610,17070,18750,23220,26270,27300,2734
50,00000,00000,00040,00260,00920,02310,04670,06830,08080,12390,17190,20980,2188
60,00000,00000,00000,00020,00110,00380,01000,01710,02170,04130,07030,10080,1094
70,00000,00000,00000,00000,00010,00040,00120,00240,00330,00790,01640,02770,0313
80,00000,00000,00000,00000,00000,00000,00010,00020,00020,00070,00170,00330,0039
900,91350,63020,38740,23160,13420,07510,04040,02600,02070,01010,00460,00230,0020
10,08300,29850,38740,36790,30200,22530,15560,11710,10040,06050,03390,02020,0176
20,00340,06290,17220,25970,30200,30030,26680,23410,21620,16120,11100,07760,0703
30,00010,00770,04460,10690,17620,23360,26680,27310,27160,25080,21190,17390,1641
40,00000,00060,00740,02830,06610,11680,17150,20480,21940,25080,26000,25060,2461
50,00000,00000,00080,00500,01650,03890,07350,10240,11810,16720,21280,24080,2461
60,00000,00000,00010,00060,00280,00870,02100,03410,04240,07430,11600,15420,1641
70,00000,00000,00000,00000,00030,00120,00390,00730,00980,02120,04070,06350,0703
80,00000,00000,00000,00000,00000,00010,00040,00090,00130,00350,00830,01530,0176
90,00000,00000,00000,00000,00000,00000,00000,00010,00010,00030,00080,00160,0020
Tabla de distribución Normal N(0,1)N(0,1) F(z)=P(Z≤z)F(z)=P(Z\leq z)
Distribución normal tipificada y área F(z) Campana normal centrada en cero. El área F(z) se sombrea desde menos infinito hasta un valor z positivo. −∞ 0 z +∞ F(z)
zz0,000,010,020,030,040,050,060,070,080,09
0,00,50000,50400,50800,51200,51600,51990,52390,52790,53190,5359
0,10,53980,54380,54780,55170,55570,55960,56360,56750,57140,5753
0,20,57930,58320,58710,59100,59480,59870,60260,60640,61030,6141
0,30,61790,62170,62550,62930,63310,63680,64060,64430,64800,6517
0,40,65540,65910,66280,66640,67000,67360,67720,68080,68440,6879
0,50,69150,69500,69850,70190,70540,70880,71230,71570,71900,7224
0,60,72570,72910,73240,73570,73890,74220,74540,74860,75170,7549
0,70,75800,76110,76420,76730,77040,77340,77640,77940,78230,7852
0,80,78810,79100,79390,79670,79950,80230,80510,80780,81060,8133
0,90,81590,81860,82120,82380,82640,82890,83150,83400,83650,8389
1,00,84130,84380,84610,84850,85080,85310,85540,85770,85990,8621
1,10,86430,86650,86860,87080,87290,87490,87700,87900,88100,8830
1,20,88490,88690,88880,89070,89250,89440,89620,89800,89970,9015
1,30,90320,90490,90660,90820,90990,91150,91310,91470,91620,9177
1,40,91920,92070,92220,92360,92510,92650,92790,92920,93060,9319
1,50,93320,93450,93570,93700,93820,93940,94060,94180,94290,9441
1,60,94520,94630,94740,94840,94950,95050,95150,95250,95350,9545
1,70,95540,95640,95730,95820,95910,95990,96080,96160,96250,9633
1,80,96410,96490,96560,96640,96710,96780,96860,96930,96990,9706
1,90,97130,97190,97260,97320,97380,97440,97500,97560,97610,9767
2,00,97720,97780,97830,97880,97930,97980,98030,98080,98120,9817
2,10,98210,98260,98300,98340,98380,98420,98460,98500,98540,9857
2,20,98610,98640,98680,98710,98750,98780,98810,98840,98870,9890
2,30,98930,98960,98980,99010,99040,99060,99090,99110,99130,9916
2,40,99180,99200,99220,99250,99270,99290,99310,99320,99340,9936
2,50,99380,99400,99410,99430,99450,99460,99480,99490,99510,9952
2,60,99530,99550,99560,99570,99590,99600,99610,99620,99630,9964
2,70,99650,99660,99670,99680,99690,99700,99710,99720,99730,9974
2,80,99740,99750,99760,99770,99770,99780,99790,99790,99800,9981
2,90,99810,99820,99820,99830,99840,99840,99850,99850,99860,9986
3,00,99870,99870,99870,99880,99880,99890,99890,99890,99900,9990
3,10,99900,99910,99910,99910,99920,99920,99920,99920,99930,9993
3,20,99930,99930,99940,99940,99940,99940,99940,99950,99950,9995
3,30,99950,99950,99950,99960,99960,99960,99960,99960,99960,9997
3,40,99970,99970,99970,99970,99970,99970,99970,99970,99970,9998
3,50,99980,99980,99980,99980,99980,99980,99980,99980,99980,9998
3,60,99980,99980,99990,99990,99990,99990,99990,99990,99990,9999
3,70,99990,99990,99990,99990,99990,99990,99990,99990,99990,9999
3,80,99990,99990,99990,99990,99990,99990,99990,99990,99990,9999
3,91,00001,00001,00001,00001,00001,00001,00001,00001,00001,0000