问题 解答题

某商场搞促销,当顾客购买商品的金额达到一定数量之后可以抽奖,根据顾客购买商品的金额,从箱中(装有4只红球,3只白球,且除颜色外,球的外部特征完全相同)每抽到一只红球奖励20元的商品,每抽到一只白球奖励10元的商品(当顾客通过抽奖的方法确定了获奖商品后,即将小球全部放回箱中).

(1)当顾客购买金额超过500元而少于1000元(含1000元)时,可从箱中一次随机抽取3个小球,求其中至少有一个红球的概率;

(2)当顾客购买金额超过1000元时,可一次随机抽取4个小球,设他所获奖商品的金额为ξ元,求ξ的概率分布列和数学期望.

答案

(1)基本事件总数n=C73=35,设事件A={任取3球,至少有一个红球},则事件

.
A
={任取3球,全是白球}.

∴P(

.
A
)=
1
35
,∵A与
.
A
为对立事件,于是

P(A)=1-P(

.
A
)=
34
35

即该顾客任取3球,至少有一个红球的概率为

34
35

(2)依题意,ξ的可能取值为50,60,70,80,

ξ=50表示所取4球为3白1红(3×10+1×20=50),

∴P(ξ=50)=

C33
C14
C47
=
4
35

ξ=60表示所取4球为2白2红(2×10+2×20=60),

∴P(ξ=60)=

C23
C24
C47
=
18
35

ξ=70表示所取4球为3红1白(3×20+1×10=70),

∴P(ξ=70)=

C43•C31
C74
=
12
35

ξ=80表示所取4球全为红球(4×20=80),

∴P(ξ=80)=

C44
C74
=
1
35

于是ξ的分布列为:

ξ50607080
P
4
35
18
35
12
35
1
35
∴Eξ=50×
4
35
+60×
18
35
+70×
12
35
+80×
1
35
=
440
7
(元).

即该顾客获奖的期望是

440
7
≈63(元).

句型转换
阅读理解

London--A morning train rides away, across the channel. English kids discuss the Liverpool's football team in a Paris pub.

Some Parisians have started to travel to work in London.

In the 19th century, Charles Dickens compared the two cities, London and Paris, in A Tale of Two Cities. These days, it might be A tale of One City.

As there are few jobs at home over recent years, perhaps 250,000 Frenchmen moved across the channel. With an undersea tunnel, they could travel between cities in three hours. The European Union freed them from immigration and customs.

Paris, rich in beauty, is more stylish. But London feels more full of life, and more fun until the pubs shut down.

“For me, the difference is that London is real, alive,” said Trevor Wheeler, a financial expert.

Chantal Jaouen, a professional designer, agrees. “I am French, but I’ll stay in London,” she said.

There is, of course, the other view. Julie Lenoux is a student who moved to London two years ago. “I think people laugh more in Paris,” she said.

“Both cities have changed beyond recognition,” said Larry Collins, an author and sometimes a Londoner. Like most people who know both cities well, he finds the two now fit together comfortably. “I first fell in love with Paris in the 1950s. Things are so much more ordered, and life is better.”

But certainly not cheaper. In some parts of London, rents can be twice those on Avenue Foch in Paris.

Deciding between London and Paris requires a lifestyle choice. Like Daphne Benoit, a French journalism student with perfect English, many young people are happy to be close enough so they don’t have to choose. “I love Paris, my little neighborhood, the way I can walk around a centre, but life is too organized,” she said. “In London, you can be whoever you want. No one cares.”

小题1:It can be inferred that ___________.

A.Paris and London are the two biggest cities in the world

B.In the 19th century, Dickens told his stories in the two cities

C.London and Paris used to be separated

D.Liverpool is a big city in France小题2:According to this passage, which of the following is TRUE?

A.People feel it difficult to find a job in Paris.

B.People can't travel to London without a passport.

C.Living in France is more expensive than in London.

D.People can find any job in London.小题3:The underlined phrase in Para9 most probably means “_____________”

A.beyond one’s imagination

B.so much that people don’t know them well again

C.so little that people still know them well

D.to people’s satisfaction小题4:What’s the meaning of the last two sentences?

A.People can do everything in London.

B.People will feel lonely in London.

C.People in London enjoy living in different ways.

D.People in London enjoy a lawless life.