问题 解答题

某商场推出二次开奖活动,凡购买一定价值的商品可以获得一张奖券.奖券上有一个兑奖号码,可以分别参加两次抽奖方式相同的兑奖活动.如果两次兑奖活动的中奖概率都是0.05,求两次抽奖中以下事件的概率:(1)都抽到某一指定号码; 

(2)恰有一次抽到某一指定号码;

(3)至少有一次抽到某一指定号码.

答案

(1)记“第一次抽奖抽到某一指定号码”为事件A,“第二次抽奖抽到某一指定号码”为事件B,

则“两次抽奖都抽到某一指定号码”为事件AB,由于两次抽奖结果互不影响,因此A与B相互独立.于是由独立性可得,

两次抽奖都抽到某一指定号码的概率为P(AB)=P(A)P(B)=0.05×0.05=0.0025;

(2)“两次抽奖恰有一次抽到某一指定号码”可以用(A

.
B
)∪(
.
A
B
)表示,由于事件A
.
B
.
A
B
互斥,

根据概率加法公式和相互独立事件的定义,所求的概率为P(A

.
B
)+P(
.
A
B
)=P(A)P(
.
B
)+P(
.
A
)P(B)

=0.05×(1-0.05)+(1-0.05)×0.05=0.095;

(3)“两次抽奖至少有一次抽到某一指定号码”可以用(AB)∪(A

.
B
)∪(
.
A
B
)表示,

由于事件AB,A

.
B
.
A
B
两两互斥,根据概率加法公式和相互独立事件的定义,

所求的概率为P(AB)+P(A

.
B
)+P(
.
A
B
)=0.0025+0.095=0.0975.

阅读理解

     Visitors to Britain are sometimes surprised to learn the newspapers there have such a large circulation(发行量). The Daily Mirror and the Daily Express both sell about four million copies every day. British

families generally buy a newspaper every morning and two or three on Sundays.

      Besides the national papers, there is, however, another branch of the British press which sells almost

as many copies. Local newspapers have a weekly circulation of 13 million. Almost every town and

country area has one. Nearly all of them hold their own finance(财政) and many of them are very

profitable.

      These papers are written almost entirely for readers interested in local events-births, weddings,

deaths, council(议会) meetings and sports. Editors prefer to depend on people who know the district

well. A great deal of local. news is regularly supplied by clubs and churches in the neighborhood and it

does not get out of date as quickly as national news.

     The editors must never forget that the success of any newspaper depends on advertising. They are

usually anxious to keep the good will of local businessmen for this reason. But if the newspaper is well

written and the news items have been carefully chosen to draw local readers, the businessmen are

grateful for the chance to keep their products in the public eyes.         

1. Local newspapers have

A. a circulation as large as that of national newspapers

B. a daily circulation of 13 million

C. a slightly smaller circulation

D. an even larger circulation

2. Which of the following is TRUE?

A. Every town and country area has at least one paper of its own.

B. Nearly all towns and country areas have their own papers.

C. There is a paper, national or local, in each town and country area.

D. A lot of distant town and country areas do not have their own papers.

3. In the writer's opinion, the editor must remember that no paper can possibly succeed without         .

A. advertisements

B. interesting reports

C. a great deal of national news

D. an excellent sales manager

4. Which of the following is NOT true?

A. A great deal of local news is supplied by the clubs and churches.

B. Local readers are much interested in local news.

C. These papers are written almost entirely for local readers.

D. These papers are likely to get out of date quickly.

单项选择题