概率论与数理统计教程(第二? 魏宗?第一?- 百度文库 ر

P(BA)?P(AB)0.2??0.5 P(A)0.4P(BA)?0.5ʱP(AB)?0.2

P(AB)?P(AB)?0.25. P(B)1.27 ˵¼A,BP(A)P(AB)֮ûй̶ĴСϵ

⣺P(A)?P(B)?0.50?P(AB)?0.5P(AB)?P(AB)?2P(AB)

P(B)ԵP(AB)?0.25ʱ,P(AB)?P(A).

0?P(AB)?0.25ʱ,P(AB)?P(A). 0.25?P(AB)?0.5ʱ,P(AB)?P(A).

1.28 nʵķʽ˭һŵӰƱʣ

(1)֪ǰk?1(k?n)˶ûkĸʣ (2)k(k?n)ĸʡ

Aiʾi i?1,2,?,n (1) P(Ak|A1?Ak?1)?11?

n?(k?1)n?k?1n?1n?211????? nn?1n?k?1n1.29 װ1n-1ÿδһ򣬲УʵkĸǶ٣

(2) P(Ak)?P(A1?Ak?1Ak)?⣺AΪkAʾkIJǰ򣬼ôǰ

?n?1?k-1ȫΪôP(A)????n?(n?1)k?1P(A)?1?P(A)?1? knk?11(n?1)k?1 ?nnk1.30 ֪һĸkĸΪ

?kk!e??(??0)ÿһܷС

(?p)r??peĸΪp֤һĸǡrһСĸΪ r! Akʾĸk Bʾĸǡrһ

P(B)??P(Ak)P(B|Ak)??k?rk?r???ke??k!?Ckr?pr(1?p)k?r

(?p)r???[?(1?p)]k?r(?p)r???[?(1?p)]n?e??e?r!(k?r)!r!n!k?rn?0

(?p)r???(1?p)(?p)r??p?e?e?e

r!r! 1.31 ijС鹲20֣һ4ˣ8ˣ

7ˣļһˣһļͨѡνĸʷֱ0.90.70.50.2һѡһ֣ͨѡνĸʡ

AkʾѡһΪk k?1,2,3,4Bʾѡһܽ

P(B)??P(Ak)P(B|Ak)?4?0.9?8?0.7?7?0.5?1?0.2?0.645

k?1420202020

1.32 ijij괲ĥٴ̨֮Ϊ9:3:2:1һʱҪĸ֮Ϊ1:2:3:1һ̨Ҫʱ̨dzĸǶ٣

A1,A2,A3,A4ֱʾ괲ĥٴBʾһҪ

9321 P(A2)? P(A3)?P(A4)? 151515151231P(B|A1)?P(B|A2)?P(B|A3)?P(B|A4)?

7777ɱʱҶ˹ʽ P(A|B)?P(A1)P(B|A1)?9 P(A1)?1?P(A)P(B|A)kkk?14221.33 P(AB)?0.5,P(BA)?0.4P(A)?0.6P(AB)¼A¼B

ǷΪʲô ⣺P(BA)?P(AB)?0.4P(A)?0.6֪P(AB)?0.24 P(A)P(AB)?P(AB)?0.5,֪P(B)?0.48 P(B)P(AB)?P(A)?P(B)?P(AB)?0.6?0.48?0.24?0.84

ΪP(A)P(B)?0.288P(AB)?0.24P(A)P(B)?P(AB) AB໥

1.34 A,B໥֤: ?,A,A,?еκһ¼?,B,B,?еκһ¼໥ġ

֤ΪP(?)?0,P(?)?1һ¼CC??,A,A,B,B,?

ΪP(???????C)?P(?)?0,P(?)P(C)?0?P(C)?0,P(?C)?P(?)P(C)?0

?κ¼

ΪP(?C)?P(C)P(?)P(C)?1?P(C)?P(C)P(?C)?P(?)P(C) ?κ¼

ΪA,BP(AB)?P(A)P(B)?P(A)(1?P(B))?P(A)?P(A)P(B)

?P(A)P(B)?P(A)?P(AB)?P(A?B)?P(AB),AB໥

AB໥֤. ͬAB1.35 ֤¼ABCA?BABA?BC

֤ 1P((A?B)C)?P(AC)?P(BC)?P(ABC)=P(A?B)P(C) 2PABC)?P(A)P(B)P(C)?P(AB)P(C)

3P((A?B)C)?P((A?AB)C)?P(AC?ABC)?P(AC)?P(ABC)

=P(A?B)P(C)

1.36A,BΪ໥¼P(A)?P(B)?1,֤P(AB)?֤ΪP(A)?P(B)?1P(A)P(B)?3 411P(A)?P(B)?ʱȺų 421ΪA,BǺP(AB)?P(A)P(B)?

43P(AB)?P(A)?P(B)?P(AB)=1?P(AB)?.

41.37 ֪¼A,B໥һݣmin(P(A),P(B))עmin(x,y)ʾx,yСһ

⣺ΪA,B໥P(A)P(B)?P(AB)A,BݣAB??

P(A)P(B)?P(AB)?0P(A),P(B)һ0

min(P(A),P(B))?0.

1.38 Ծ˵P(ABC)?P(A)P(B)P(C)ƳP(AB)?P(A)P(B)һ

??{?1,?2,?3,?4,?5}P({?1})?P({?2})? P({?3})?P({?4})?118P({?5})? 646415A?{?1,?2}B?{?1,?3}C?{?1,?4} 641151 P(A)?P(B)?P(C)???

646441 P(ABC)?P({?1})??P(A)P(B)P(C)

641P(AB)?P({?1})??P(A)P(B).

641.39 ໥¼A,B,C

19ABC??,P(A)?P(B)?P(C)?֪P(ABC)?P(A)

216⣺A,B,C໥ȣP(AB)?P(BC)?P(AC)?P(A) ABC??P(ABC)?0

2P(ABC)?P(A)?P(B)?P(C)?P(AB)?P(AC)?P(BC)?P(ABC)=3P(A)?3P2(A)?931,P(A)?(ȥ)P(A)? 16441.40 һ˵ѪΪO,A,B,AB͵ĸʷֱΪ0.460.400.110.03ѡˣ¼ĸ

(1)ΪOͣ˷ֱΪѪͣ (2)ΪOͣΪAͣ(3)ûһΪAB

(1)5ѡ2ΪOͣC52ֿܣ3ѡһΪ

Aֿͣܣµ2ѡһΪBͣ2ֿܣһΪABͣ˳ΪC52?3?2?0.462?0.40?0.11?0.13?0.0168

3?0.463?0.402?0.1557 (3) (1?0.03)5?0.8587 (2) C5