问题 问答题

甲、乙、丙三人同时独立地向同一目标射击,各打一发子弹,命中率分别为0.4,0.5和0.6,目标中一、二、三弹而被击毁的概率分别为0.2,0.4和0.8.
(Ⅰ) 求目标被击毁的概率P;
(Ⅱ) 已知目标被击毁,求目标中三弹的概率q.

答案

参考答案:设A表示事件“目标被击毁”,Bi表示事件“目标中i弹”(i=0,1,2,3),由事件的独立性,得
P(B0)=(1-0.4)(1-0.5)(1-0.6)=0.12,
P(B1)=0.4×(1-0.5)(1-0.6)+(1-0.4)×0.5×(1-0.6)+(1-0.4)(1-0.5)×0.6
=0.38,
P(B2)=0.4×0.5×(1-0.6)+0.4×(1-0.5)×0.6+(1-0.4)×0.5×0.6=0.38,
P(B3)=0.4×0.5×0.6=0.12.
事件B0,B1,B2和B3是该随机试验的完备事件组.
(Ⅰ)根据全概率公式,得


(Ⅱ)根据贝叶斯公式,得

解析:

[分析]: 目标中一弹有三种情形:甲击中目标而乙和丙未击中;乙击中目标而甲和丙未击中;丙击中目标而甲和乙未击中.目标中二弹也有三种情形,而目标中三弹只有一种情形.没有一弹击中目标也只有一种情形,且此时目标肯定没有被击毁.利用独立性可求得目标中i(i=0,1,2,3)弹的概率,利用全概率公式可求得p,利用贝叶斯公式可求得q.

阅读理解

阅读理解。

     Mr. White was in bed and was trying to go to sleep when he heard the doorbell ring. He turned on the

light and looked at the clock. It was half past twelve. "Who can be it at this time of night?" he wondered.

He decided to go and find out. So he got out of bed, put on his jacket and went to the door. When he opened

the door, there was nobody there. "That's very strange," he thought. Then he went back to his bedroom, took

off his jacket, got back into bed, turned off the light and tried to go to sleep.

     A few minutes later he heard the doorbell ring again. Mr. White jumped out of the bed very quickly and

rushed to the door. He opened it, but again he found no one there. He closed the door and tried not to feel too

nervous. Then he saw a piece of paper on the floor inside the door. He picked it up. There were some words

on it: "Now it's after midnight, so it's April 1st. Happy April Fool's Day!"

     "Oh, it was the funny boy next door!"  Mr. White smiled.

1. Mr. White was trying to go to sleep when he heard _____. [ ]

A. somebody sing

B. the doorbell ring

C. the telephone ring

D. somebody knock at the window

2. At first Mr. White turned on the light and _____. [ ]

A. got out of the bed

B. put on his jacket

C. wanted to know the time

D. called the police 

3. When he opened the door at the first time, he found _____ outside the door. [ ]

A. no one

B. a boy

C. his friend

D. a piece of paper

4. The story happened _____. [ ]

A. At noon

B. at twelve

C. on April 2nd

D. on April 1st

5. The boy rang the doorbell because he wanted to _____. [ ]

A. borrowed Mr. White's clock

B. ask Mr. White for a piece of paper

C. make fun of Mr. White

D. tell Mr. White a story

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