问题 解答题
随着建设资源节约型、环境友好型社会的宣传与实践,低碳绿色的出行方式越来越受到追捧,全国各地兴起了建设公共自行车租赁系统的热潮,据不完全统计,已有北京、株洲、杭州、太原、苏州、深圳等城市建设成公共自行车租赁系统,某市公共自行车实行60分钟内免费租用,60分钟以上至120分钟(含),收取1元租车服务费,120分钟以上至180分钟(含),收取2元租车服务费,超过180分钟以上的时间,按每小时3元计费(不足一小时的按一小时计),租车费用实行分段合计.现有甲,乙两人相互独立到租车点租车上班(各租一车一次),设甲,乙不超过1小时还车的概率分别为
1
2
1
4
,1
小时以上且不超过2小时还车的概率分别为
1
4
1
3
,2
小时以上且不超过3小时还车的概率分别为
1
8
1
3
,两人租车时间均不会超过4小时.
(1)求甲、乙两人所付租车费用相同的概率.
(2)设甲一周内有四天(每天租车一次)均租车上班,X表示一周内租车费用不超过2元的次数,求X的分布列与数学期望.
答案

(1)甲、乙两人租车费用相同包括0,1,3,6元

两人都付0元的概率为P1=

1
2
×
1
4
=
1
8

两人都付1元的概率为P2=

1
4
×
1
3
=
1
12

两人都付3元的概率为P3=

1
8
×
1
3
=
1
24

两人都付6元的概率为P4=(1-

1
2
-
1
4
-
1
8
)×(1-
1
4
-
1
3
-
1
3
)=
1
8
×
1
12
=
1
96

则甲,乙两人所付租车费用相同的概率为P=P1+P2+P3+P4=

25
96

(2)依题意,甲某每天租车费用不超过2元的概率为P=

1
2
+
1
4
=
3
4

则P(X=0)=

C04
×(
3
4
)0
×(
1
4
)
4
=
1
256
,P(X=1)=
C14
×(
3
4
)
1
×(
1
4
)
3
=
3
64

P(X=2)=

C24
×(
3
4
)
2
×(
1
4
)
2
=
27
128
,P(X=3)=
C34
×(
3
4
)
3
×(
1
4
)
1
=
27
64

P(X=4)=

C44
×(
3
4
)
4
×(
1
4
)
0
=
81
256

∴X的分布列为

 X 0 1 2 3
 P 
1
256
 
3
64
 
27
128
 
27
64
81
256
 
X的数学期望为E(X)=1×
3
64
+2×
27
128
+3×
27
64
+4×
81
256
=3

阅读理解

阅读理解。

     CCTV images were released today of a suspected rapist who attacked a woman in Glasgow city

center.

     Detectives have issued pictures of a man in a bid to catch the sex attacker who struck last month.

     The man is said to have scars on his forehead and chest and a tattoo() on his right arm.

     The attack took place in the early hours of Saturday, April 18, on waste ground between Carrick

Street and Broomielaw. Although the 27-year-old victim was not injured, she was left badly shaken. Her

attacker was last seen running in Argyle Street near to Cadogan Street.

     The man the police wish to speak to is described as a white male, aged around 20 and 5ft 6in tall. He

has a tanned complexion(黄褐色面肤), short gelled hair, muscular build(肌肉发达) with a scar on the

right side of his forehead. He is wearing a white T-shirt, light blue jeans with cargo pockets and white

training shoes.

     Detective Inspector Andy Mc William, of Stewart Street CID, said, "Today we're issuing CCTV

images of a male pictured in a city center street in the early hours of Saturday, April 18. He may be able

to assist us in our investigation. I would ask him, or any person who recognizes him, to come forward. I'd

also ask anyone who was in the general areas of Broomielaw or Carrick Street on the night in question

and saw this man or has any information that may assist us to contact me/"

     Anyone who can help should contact Stewart Street CID on 0141 532 3116 or Crime stoppers on

0800 555 111 where anonymity can be maintained.

1. What can the man who offers the information about the sex attacker get in reward?

A. Appearance on television.

B.  Images of some detectives.

C.  Money for his action.

D.  A scar on the forehead.

2. The underlined word in the last paragraph probably means __________.

A. a person who is unwilling to offer his or her personal information

B. a person who can make great contributions to certain affairs

C. a person who wants to get rewards and offers help to the police

D. a person who gives away his friend to get a higher position

3. Why did Andy Mc William say those words in the last but one paragraph?

A. He wished to get help from society.

B. He wanted anyone to have contact with him.

C. He hoped to observe the people watching the TV.

D. He told the society why they were issuing CCTV images.

4. What advantage do you have when you phone the number 0800 555 111?

A. You can contact Stewart Street CID freely.

B. You can communicate with Crime Stoppers.

C. All your information may be exposed to the public.

D. The public will not know anything about your own information.

单项选择题