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1、 Probability and Statistics Chapter 1 Random Events and Probability1Tests Probability and Statistics Chapter 1 Random Events and Probability2()0.6,()0.4,P AP B ()0.01,()0.02,P C AP C B () ()()() ()() ()P A P C AP A CP A P C AP B P C B 0.60.010.60.010.40.0237 Probability and Statistics Chapter 1 Rand

2、om Events and Probability3Review復習()(|)( )P ABP B AP A ()( )P ABP A P B A 1()() ()niiiP BP A P B A 1(|)()()()()jjjniiiP ABP AP B AP A P B A Probability and Statistics Chapter 1 Random Events and Probability4 Chapter 1 Random Events and Probability Content Probability and Statistics Chapter 1 Random

3、Events and Probability5教學要求教學要求 1.4 隨機事件的獨立性隨機事件的獨立性 主要內容主要內容ContentsRequests Chapter 1 Random Events and Probability Independence of Events Probability and Statistics Chapter 1 Random Events and Probability6Mutual Independence of Events ( ),( ),(),()P A P B P AB P B A()()P AP B 42105 P AB 444101025

4、4522525( )P B P ABP B AP A P ABP A P B Probability and Statistics Chapter 1 Random Events and Probability7The Definition of Mutual Independent two Events PABPA PB 事件事件A與事件與事件B相互不影響對方發生相互不影響對方發生 假設假設 那么那么假設假設 那么那么A 與與 B 相互獨立相互獨立()0, ()()P AP BP B A ()0, ()()P BP AP A B Probability and Statistics Chap

5、ter 1 Random Events and Probability8 PB APB 0,PA P ABP A P B P ABP B AP A P A P BP BP A PB APB P ABP A P B AP A P B Probability and Statistics Chapter 1 Random Events and Probability91)“A與與 B相互獨立和相互獨立和 “A 與與 B 互斥互斥 有關系嗎？有關系嗎？2)在普通情形下在普通情形下 兩者有關系嗎？兩者有關系嗎？ 0,0,P AP B ()( ) ( )P ABP A P B AB A與與B 獨立獨立,

6、那么那么AB 0P A 0P B Probability and Statistics Chapter 1 Random Events and Probability10ABAB()( ) ( )P ABP A P B ()( ) ( )P ABP A P B ()( ) ( )P ABP A P B ()( ) ( )P ABP A P B Probability and Statistics Chapter 1 Random Events and Probability11()( ) ( )P ABP A P B ()P ABP AB( ) ( )P A P B P AP A P B AB

7、 ( ) 1P AP B P AP AB Probability and Statistics Chapter 1 Random Events and Probability12 AB ()( ) ( )P ABP A P B ()P ABP AAB P AP A P B ( ) 1P AP B P AP AB ( ) ( )P A P B B B Probability and Statistics Chapter 1 Random Events and Probability13The Definition of Mutual Independent three Events ()( )

8、( ) (1)()( ) ( ) (2)()( ) ( ) (3)()( ) ( ) ( ) (4)P ABP A P BP BCP B P CP ACP A P CP ABCP A P B P C Probability and Statistics Chapter 1 Random Events and Probability14The Definition of Mutual Independent n Events 121212121211() 1mmijijijkijkiiiiiimnnP AAP A P Aij nP AAAP A P A P Aij k nP A AAP A P

9、AP AiiinP AAAP A P AP A 12， ， ，AAAn12， ， ，AAAn Probability and Statistics Chapter 1 Random Events and Probability15 設有甲乙兩個射手，他們每次射擊命設有甲乙兩個射手，他們每次射擊命中目的的中目的的 概率分別是概率分別是0.8和和0.7現兩人同現兩人同時向一目的射擊一次，時向一目的射擊一次， 試求：試求： 1目的命中的概率；目的命中的概率；2假設知目的被命中，那么它是甲命假設知目的被命中，那么它是甲命中的概率是多少？中的概率是多少？ 解解 設設A=甲命中目的甲命中目的, B=乙命中

10、目的乙命中目的C=命中目的命中目的, CAB Probability and Statistics Chapter 1 Random Events and Probability16( )()( )( )()P CP ABP AP BP AB( )( )( ) ( )P AP BP A P B0.80.70.8 0.7 0.94 ()( )0.840()( )( )0.9447P ACP AP A CP CP C Probability and Statistics Chapter 1 Random Events and Probability17iA123123123( )()P AP A

11、A AA A AA A A 123123123() () ()() () ()() () ()P A P A P AP A P A P AP A P A P A 15% 80% 75% 85% 20% 75% 85% 80% 25% 9%12.75%17%38.75% Probability and Statistics Chapter 1 Random Events and Probability18(2) 設設 123( )()P BP AAA 1231()P A A A 1231() () ()P A P A P A 49% 185%80%75% 1231()P AAA Probabil

12、ity and Statistics Chapter 1 Random Events and Probability19Bernoulli Probability and Binomial Probability Formula ( ), 01P App ,A A Probability and Statistics Chapter 1 Random Events and Probability20( )(01),P App iA()( )iP AP Ap 123123123( )()P BP A A AA A AA A A 123123123() () ()() () ()() () ()P

13、 A P A P AP A P A P AP A P A P A 23(1)pp 2213(1)C pp Probability and Statistics Chapter 1 Random Events and Probability21定理定理3 設在每次實驗中，設在每次實驗中，p (0p1), 即即 P(A)=p, ()1P Ap 事件事件A發生的概率為發生的概率為( )(1),0,1,2,kkn knnP kC ppkn Binomial Probability Formula 0nnkkn knkabC a b 00(1)( )11nkkn knknnnkC pPkppp Prob

14、ability and Statistics Chapter 1 Random Events and Probability22( )(1),0,1,2,kkn knnP kC ppkn Probability and Statistics Chapter 1 Random Events and Probability23145512(1)( )( )0.329233PC 0055121( ) ( )0.868333C 5( )1( )1(0)P BP BP 55()(0)(1)P CPP 005114551212( ) ( )( ) ( )0.46093333CC Probability a

15、nd Statistics Chapter 1 Random Events and Probability24001(1)1(1)1(1)nkkn knnnnkC ppC ppp 1(1)np001111(1)(1)(1)(1)nnnnnnC ppC pppnpp 1(1)(1)nnpnpp Probability and Statistics Chapter 1 Random Events and Probability25192713001(1)1(1)1 (1)nkkn knnnnkC ppC ppp 331981(1)(1)2727pp 13p Probability and Statistics Chapter 1 Random Events and Probability26(01)p23 (1)pp 26 (1)pp 223(1)pp 226(1)pp 1223

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