问题 解答题
袋中共有10个大小相同的编号为1、2、3的球,其中1号球有1个,2号球有m个,3号球有n个.从袋中依次摸出2个球,已知在第一次摸出3号球的前提下,再摸出一个2号球的概率是
1
3

(1)求m,n的值;
(2)从袋中任意摸出2个球,设得到小球的编号数之和为ξ,求随机变量ξ的分布列和 数学期望Eξ.
答案

(1)记“第一次摸出3号球”为事件A,“第二次摸出2号球”为事件B,

P(B|A)=

m
9
=
1
3
,…(4分)

∴m=3,n=10-3-1=6…(5分)

(2)ξ的可能的取值为3,4,5,6.…(6分)

P(ξ=3)=

1•
C13
C210
=
1
15
,P(ξ=4)=
1•
C16
+
c23
C210
=
1
5
P(ξ=5)=
C13
C16
C210
=
2
5
,P(ξ=6)=
C26
C210
=
1
3
.…(10分)

∴ξ的分布列为

ξ 3 4 5 6
P
1
15
1
5
2
5
1
3
Eξ=3×
1
15
+4×
1
5
+5×
2
5
+6×
1
3
=5
.…(12分)

选择题
阅读理解

When the six very best students from different cities in Guangdong Province all together chose universities in Hong Kong ; when the very best students of Beijing picked up HK University while giving up the nearby Peking or Tsinghua University ; when the highest enrollment(录取) rate of Hong Kong Science and Industry University reached 48:1, it’s the high time to ask where the real education heaven for students in China is.

Years ago, the answer certainly would be “Peking or Tsinghua University”. But now no one could give the exact answer without hesitation . The only sure thing is that HK universities have gradually showed an unusual attraction to a great many mainland students.

There’s no doubt to call this HK craze (狂热), which is even out of the expectation of those HK universities themselves.

How can HK universities shake the steady foundations of Peking and Tsinghua University and attract so many mainland students?

First, Hong Kong universities offer large-amount scholarship, especially for the top students who can receive the scholarship as much as 400,000 HK dollars. Since higher education has become a kind of heavy burden of many families, it’s easy to understand why the reaction to the generous offering of HK universities is great.

Second, most HK universities receive professors and students from all over the world and carry out bilingual (双语) education. This kind of excellent language atmosphere is another attraction for mainland students.

Furthermore, university students in Hong Kong have a better chance to study abroad as exchange students.

Can mainland top universities like Peking or Tsinghua University be calm as before when facing the unexpected competition from HK? Will they take relevant measures to win back the top students who once help them set the worldwide reputation? Time will explain it .

The fierce competition brought by HK universities can be a good thing for an entire improvement of education in China. After the awakening and action-taking of mainland universities , they can perform better together with HK universities.

At least, it reminded the mainland universities the tuition fees (学费) are among students’ top concern when they are choosing universities . It’s time to move.

小题1:What is the passage mainly talking about?

A.Some thoughts brought by the enrollment of HK universities.

B.Higher education in Hong Kong.

C.The competition between HK University and Beijing University.

D.The fall of mainland universities.小题2:Top students from mainland apply for HK universities because________.

A.many students now would love to study abroad to get a better experience

B.they concern only about the tuition fees when choosing universities

C.HK Universities offer higher scholarship, better environment and more opportunities for their further study

D.Beijing University has lost its worldwide reputation小题3:   From the passage we can see HK universities________.

A.didn’t mean to enroll top students from mainland

B.didn’t expect their enrollment of mainland students would be so popular

C.have strict enrollment rules and only 1 out of 48 students can get the chance to study there

D.are proud of their teaching staff and facilities.小题4:What does the author mean by saying “It’s time to move .” in the last paragraph ?

A.Mainland universities should take measures as soon as possible to attract students.

B.The opportunities come for top students to study abroad .

C.Mainland universities should make full preparations to enroll Hong Kong students .

D.Top students should be offered further education free of charge .