问题 解答题
在一次数学考试中,第21题和第22题为选做题.规定每位考生必须且只须在其中选做一题.设4名考生选做每一道题的概率均为
1
2

(1)求其中甲、乙两名学生选做同一道题的概率;
(2)设这4名考生中选做第22题的学生个数为ξ,求ξ的概率分布及数学期望.
答案

(1)设事件A表示“甲选做第21题”,事件B表示“乙选做第21题”,

则“甲选做第22题”为

.
A
,“甲选做第22题”为
.
B

进而可得,甲、乙2名学生选做同一道题的事件为“AB+

.
A
.
B
”,且事件A、B相互独立.

P(AB+

.
A
.
B
)=P(A)P(B)+P(
.
A
)P(
.
B
)=
1
2
×
1
2
+(1-
1
2
)×(1-
1
2
)=
1
2

(2)随机变量ξ的可能取值为0,1,2,3,4,且ξ~B(4,

1
2
).

P(ξ=k)=

Ck4
(
1
2
)k(1-
1
2
)4-k=
Ck4
(
1
2
)4
(k=0,1,2,3,4)

∴变量ξ的分布列为:

Eξ=0×

1
16
+1×
1
4
+2×
3
8
+3×
1
4
+4×
1
16
=2(或Eξ=np=4×
1
2
=2
).

阅读理解

阅读理解。

     These days, more and more students in the UK are taking a "gap year" between their graduation

from school arid their university studies. This means that they take a year off, to do something else,

before they start their studies.

     For most students,  spending time in foreign countries is the favorite activity-and Australia is the

favorite place to go.

     Many parents,  teachers and business people agree that traveling can teach important values.

     "After a year of travcling, I felt I'ci grown up. I had learnt the importance of relationships with people, 

on all sorts of levels. "

     There arc many companies around the world that welcome these students on their projects hclping

people in poorer countries, or even in your home country.  Although you don't get paid for your work, 

this

kind of work can teach important skills-decision making and finding answers to problems.  for cxample

that will help a student in a job one day.

     Finally,  getting some knowledge and experience in an area you hope to study or work in one day

will always bc very useful.

     If several university graduates are applying for the same job, gap year work cxperience allows you

to say:  "I've already had some experience of this kind of work. "

     And that can get you the job!

根据短文内容,判断句子正(T)误(F)。

( )1. These days,  all students in the UK take a gap year.

( )2. Traveling can teach you values such as learning about relationships.

( )3. Working on projects in poorer countries is all about managing people.

( )4. Students will get paid well for their work when they help the poorer people.

( )5. University graduates with some work experience often get jobs more easily than graduates 

           without experience.

填空题