问题 解答题

(理)某市准备从6名报名者(其中男4人,女2人)中选3人参加三个副局长职务竞选.

( I)求男甲和女乙同时被选中的概率;

( II)设所选3人中女副局长人数为ξ,求ξ的分布列及数学期望;

( III)若选派三个副局长依次到A,B,C三个局上任,求A局是男副局长的情况下,B局为女副局长的概率.

答案

( I)所有不同的选法共有

C36
种,

其中男甲和女乙同时被选中的选法有

C14
种,

则男甲和女乙同时被选中的概率为

C14
C36
=
1
5

( II)ξ的所有可能取值为0,1,2.

依题意得P(ξ=0)=

C34
C36
=
1
5

P(ξ=1)=

C12
?
C24
C36
=
3
5

P(ξ=2)=

C22
C14
C36
=
1
5

∴ξ的分布列为:

ξ012
P
1
5
3
5
1
5
∴Eξ=0×
1
5
+1×
3
5
+2×
1
5
=1.

( III)设事件M=“A局是男副局长”,N=“B局是女副局长”.

则P(M)=

C14
A25
A36
=
2
3
,P(MN)=
C12
C14
C14
A36
=
4
15

所以A局是男副局长的情况下,B局为女副局长的概率为P(N/M)=

P(MN)
P(M)
=
4
15
2
3
=
2
5

阅读理解

In a world as fast-changing and full of information as our own, all of us need to know how to learn well. Yet evidence suggests that most of us don’t use the learning techniques that science has proved the most effective.

The scientific literature evaluating these techniques goes back to decades and across thousands of articles. It’s far too extensive and complex for the average parent, teacher or employer to look through. Fortunately, a team of five leading psychologists have done the job for us.

Professor John Dunlosky and other psychologists closely examined 10 learning strategies and rated each from high to low utility(实用) on the basis of the evidence they’ve gathered. Here’s part of their conclusions:

In contrast to familiar practices, the effective learning strategies with the most evidence to support them aren’t well known outside the lab. Take distributed practice, for example. This strategy involves spreading out your study time, rather than engaging in one marathon. Cramming (死记硬背)information at the last minute may allow you to get through that test or meeting, but the material will quickly disappear from your memory. It’s much more effective to look through the material at intervals over time.

And the longer you want to remember the information, whether it’s two weeks or two years, the longer the intervals should be.

The second learning strategy that is highly recommended by Dunlosky is practice testing. Yes, more tests---but there not for a grade. Research shows that the mere act of calling information to mind strengthens that knowledge and aids in future retrieval (检索). While practice testing is not a common strategy---despite the strong evidence supporting it ---there is one familiar approach that captures its benefits: using flash cards. And now flash cards can be presented in digital form. Both distributed practice and practice testing were rated as having “high utility” by Dunlosky.

小题1:How did the psychologists study and rate the learning strategies?

A.By analyzing the materials gathered in the past years.

B.By asking some students questions about their study.

C.By doing some experiments on the objects in the lab.

D.By asking parents and teachers to look through the articles.小题2:The underlined word “extensive” in Para.2 means _____.

A.small in amount

B.easy or quick to do

C.more than is needed

D.dealing with a lot of information小题3:About distributed practice and practice testing, it’s true that _____.

A.many students have benefited a lot from them

B.they were first put forward by John Dunlosky

C.only a small number of experts know about them

D.psychologists are studying whether they are effective小题4:The strategy of distributed practice shows that ______.

A.we should not study for long hours every day

B.reviewing what we have studied is of little help

C.the shorter the interval is, the better we’ll study

D.doing repetition at intervals is the best way小题5:The evidence shows that the strategy of practice testing ______.

A.is a way to use flash cards to help study

B.is mainly used to help us remember well

C.helps know about students’ grades in time

D.is a way widely used to strengthen memory

多项选择题