问题 解答题
在一个选拔项目中,每个选手都需要进行4轮考核,每轮设有一个问题,能正确回答者进入下一轮考核,否则被淘汰.已知某选手能正确回答第一、二、三、四轮问题的概率分别为
5
6
4
5
3
4
1
3
,且各轮问题能否正确回答互不影响.
(Ⅰ)求该选手进入第三轮才被淘汰的概率;
(Ⅱ)求该选手至多进入第三轮考核的概率;
(Ⅲ)该选手在选拔过程中回答过的问题的个数记为X,求随机变量X的分布列和期望.
答案

设事件Ai(i=1,2,3,4)表示“该选手能正确回答第i轮问题”,

由已知P(A1)=

5
6
P(A2)=
4
5
P(A3)=
3
4
P(A4)=
1
3

(Ⅰ)设事件B表示“该选手进入第三轮被淘汰”,

P(B)=P(A1A2

.
A
3)=P(A1)P(A2)P(
.
A
3
)=
5
6
×
4
5
×(1-
3
4
)=
1
6

(Ⅱ)设事件C表示“该选手至多进入第三轮考核”,

P(C)=P(

.
A
1+A1
.
A
2
+A1A2
.
A
3
)=P(
.
A
1
)+P(A1
.
A
2
)+P(A1A2
.
A
3
)=
1
6
+
5
6
×
1
5
+
5
6
×
4
5
×(1-
3
4
)=
1
2

(Ⅲ)X的可能取值为1,2,3,4.P(X=1)=P(

.
A
1)=
1
6
P(X=2)=P(A1
.
A
2
)=
5
6
×(1-
4
5
)=
1
6
P(X=3)=P(A1A2A3
.
A4
)=
5
6
×
4
5
×
3
4
×
1
3
=
1
6
P(X=4)=P(A1A2A3)=
5
6
×
4
5
×
3
4
=
1
2

所以,X的分布列为

E(X)=1×

1
6
+2×
1
6
+3×
1
6
+4×
1
2
=3.

填空题
单项选择题

In order to understand, however imperfectly, what is meant by "face", we must take (1) of the fact that, as a race, the Chinese have a ply (2) instinct. The theatre may almost be said to be the only national amusement, and the Chinese have for theatricals a (3) like that of the Englishman (4) athletics, or the Spaniard for bull-fights. Upon very slight provocation, any Chinese regards himself in the (5) of an actor in a drama. He throws himself into theatrical attitudes, performs the salaam, falls upon his knees, prostrates himself and strikes his head upon the earth, (6) circumstances which to an Occidental seem to make such actions superfluous, (7) to say ridiculous. A Chinese thinks in theatrical terms. When roused in self-defense he addresses two or three persons as if they were a multitude. He exclaims: "I say this in the presence of You, and You, and You, who are all here present. " If his troubles are adjusted he (8) of himself as having "got off the stage" with credit, and if they are not adjusted he finds no way to "retire from the stage". All this, (9) it clearly understood, has nothing to do with realities. The question is never of facts, but always of (10) . If a fine speech has been (11) at the proper time and in the proper way, the requirement of the play is met. We are not to go behind the scenes, for that would (12) all the plays in the world. Properly to execute acts like these in all the complex relations of life, is to have "face". To fail them, to ignore them, to be thwarted in the performance of them, this is to " (13) face". Once rightly apprehended, "face" will be found to be in itself a (14) to the combination lock of many of the most important characteristics of the Chinese.

It should be added that the principles which regulate "face" and its attainment are often wholly (15) the intellectual apprehension of the Occidental, who is constantly forgetting the theatrical element, and wandering (16) into the irrelevant regions of fact. To him it often seems that Chinese "face" is not unlike the South Sea Island taboo, a force of undeniable potency, but capricious, and not reducible to rule, deserving only to be abolished and replaced by common sense. At this point Chinese and Occidentals must agree to (17) , for they can never be brought to view the same things in the same light. In the adjustment of the incessant quarrels which distract every hamlet, it is necessary for the "peace-talkers" to take a careful account of the (18) of "face" as European statesmen once did of the balance of power. The object in such cases is not the execution of even-handed justice, which, even if theoretically desirable, seldom (19) to an Oriental as a possibility, but such an arrangement as will distribute to all concerned "face" in due proportions. The same principle often applies in the settlement of lawsuits, a very large percentage of which end in what may be called a (20) game.

17()

A.disagree

B.compromise

C.settle

D.surrender