（2）P?恰有二人进球??P(ABC?ABC?ABC)
?P(ABC)?P(ABC)?P(ABC) （ABC,ABC,ABC互斥） ?P(A)P(B)P(C)?P(A)P(B)P(C)?P(A)P(B)P(C) (A,B,C相互独立）
?0.5?0.7?0.4?0.5?0.7?0.6?0.5?0.3?0.6?0.44 （3）P?至少有一人进球??P(A?B?C)
?1?P(A?B?C) ?1?P(ABC)
?1?P(A)P(B)P(C) (A,B,C相互独立） ?1?0.5?0.3?0.4 ?0.94
19、解：用Ai表示事件“第i个供血者具有A?RH?血型”，i?1,2,3,?
B表示事件“病人得救”
?B?A1?A1A2?A1A2A3?A1A2A3A4,
A1,A1A2,A1A2A3,A1A2A3A4互斥，Ai（i?1,2,3,?）相互独立 ?P(B)?P(A1)?P(A1A2)?P(A1A2A3)?P(A1A2A3A4)
?0.4?0.6?0.4?0.62?0.4?0.63?0.4?0.8704
20、解：设Ai表示事件“元件i可靠” i=1,2,3,4,5 ，B表示事件“系统可靠由已知得P(Ai)?p(i?1,2,3,4,5) A1,A2,A3,A4,A5相互独立
法1：B?A1A2?A3?A4A5
?P(B)?P(A1A2?A3?A4A5)
?P?A1A2??P?A3??P?A4A5??P?A1A2A3??P?A3A4A5??P?A1A2A4A5??P?A1A2A3A4A5?
?p2?p?p2?p3?p3?p4?p5 ?A1,A2,A3,A4,A5相互独立? 6
”
2345?2p?p?2p?p?p
法2：P(B)?1?P(A1A2A3A4A5)
?1?P(A1A2)P(A3)P(A4A5) ?A1,A2,A3,A4,A5相互独立 ?1?[1?P(A1A2)][1?P?A3?][1?P?A4A5?]
?1?[1?P(A1)P(A2)][1?P?A3?][1?P?A4?P?A5?]
?
?A1,A2,A3,A4,A5相互独立?
?1??1?p2??1?p??1?p2? ?p?2p2?2p3?p4?p5
21、解：令A：“产品真含杂质”，A：“产品真不含杂质” 则
P(A)?0.4，P(A)?0.6
2222 P(B|A)?C3?0.8?0.2 P(B|A)?C3?0.1?0.9
?P(B)?P(B|A)P(A)?P(B|A)P(A)
?C3?0.822?0.2?0.4?C3?0.1?0.9?0.6
22?P(A|B)?
P(AB)P(B)22?P(B|A)P(A)P(B|A)P(A)?P(B|A)P(A)
?C3?0.8?0.2?0.4C?0.8?0.2?0.4?C?0.1?0.9?0.6232232?256283?0.905
1、P?Y?k???1?0.4? 第二章习题答案
k?1?0.4 k=1,2,?
2、用Ai表示第i个阀门开
P{X?0}?P(A1(A2?A3))?P(A1)(P(A2)?P(A3)?P(A2)P(A3)) ?0.2(0.2?0.2?0.2?0.2)?0.072
7
P{X?1}?P[A1(A2?A3)?A1A2A3]?0.8(0.2?0.2?0.04)?0.2?0.82 ?0.416
P{X?2}?P(A1A2A3)?0.83?0.512 3、X~b?15,0.2?
P?X?k??C150.2?0.8kk15?k k=0,1,2,??,15
3312 （1）P?X?3??C150.2?0.8?0.2501
0015114 （2）P?X?2??1?C150.2?0.8?C150.2?0.8?0.8329
111422133312 （3）P?1?X?3??C150.2?0.8?C150.2?0.8?C150.2?0.8?0.6129
（4）P?X?5??1?5?Ck?0k150.2?0.8k15?k?0.0611
4、用X表示5个元件中正常工作的个数
332445 P(X?3)?C50.9?0.1?C50.9?0.1?0.9?0.9914
5、设X=?8000件产品的次品数? 则X~b(8000,0.001)
近似地由于n很大，P很小，所以利用X～?(8) P?X?7??6?k?08ek?8k!?0.3134
6、(1)X~?(10)
?P?X?15??1?P?X?15??1? (2)∵ X~?( ?) ?12?P?X?0??1?P?X?0??1?1215?k?010ek!k?10?1?0.9513?0.0487
?e0??0!
?P?X?0?? ?e??
?12 ???ln2?0.7
1 ?P?X?2??1?P?X?1??1??k?00.7ek!k?0.7?1?0.8442?0.1558
8
或P?X?2??1?P?X?0??P?X?1??1??2012?ln2e?ln21!?12?12ln2
7、(1) X~?(2) P{X?0}?e20!?e?2 ?0.1353 (2) p?C54(e?2)4(1?e?2)?0.00145
? (3) p??(k?0e?22k5k!)
18、(1) 由1??????f(x)dx??10kxdx?2k3x30?k3 ?k?3
11（2）P?X?3???3??f?x?dx??303xdx?x1321421330?127
1??1（3）P??X???2??41?2143xdx?x2?18?1643123?764
（4）P?X??2?2???3????23f(x)dx??1233xdx?x2?1?827?1927
9、方程t?2Xt?5X?4?0有实根，则 ??(2X)2?4(5X?4)?0 得 X?4或X?1.
有实根的概率 P{X?4?X?1}?1?100.003xdx??x22?1040.003xdx?0.937
1210、(1) P{X?1}??x100?0e?x2200dx??e200|?1?e210?200?0.005
2(2) P{X?52}??52100ex?x2200dx??e?x200|52??e262??52200?0
(3) P{X?26|X?20}?P{X?26}P{X?20}?ee?200202 ?0.25158?20011、解： （1）P?X?1??527???1f(x)dx??9?4?x?212113?88415?4dx??x?x??????
2792792727?9?12（2）Y~b(10，)
9
?5??22?P?Y?k??C??????27??27?k102k10?k k=0,1,2,??,10
8?22?2?5?（3）P?Y?2??C10??????0.2998
?27??27? P?Y?2??1?P?Y?0??P?Y?1? ?22?2?5? ?1?C10?????2727????0101?5??22? ?C10?????0.57782727????1912（1）由1??????f?y?dy?0?1?0?10.2dy?c21??0.2?cy?dy
01 ?0.2y?(0.2y?y)02?0.4?c2
?c?1.2 ?0.2? ?f?y???0.2?1.2y??0?1?y?00?y?1 其它FY(y)??y???y0dt?????y0.2dt????1f(t)dt??0y?0.2dy??0.2?1.2y?dy??0??1?1?0.2?1.2y?dy???0y??1?1?y?0
0?y?1y?1?0??0.2y?0.2??2?0.6y?0.2y?0.2?1?y??1?1?y?00?y?1y?12
P?0?Y?0.5??F?0.5??F?0??0.2?0.2?0.5?0.6?0.5?0.2?0.25 P?Y?0.1??1?F?0.1??1?0.2?0.2?0.1?0.6?0.1?0.774
2P?Y?0.5??1?F?0.5??1?0.2?0.2?0.5?0.6?0.5?0.55
2?P?Y?0.5Y?0.1??P?Y?0.5,Y?0.1?P?Y?0.1??P?Y?0.5?P?Y?0.1??0.550.774?0.7106
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