问题 解答题

袋中装有标号分别为1、2、3、4、5、6的卡片各1张,从中任取两张卡片,其标号分别记为x、y(其中x>y).

(1)求这两张卡片的标号之和为偶数的概率;

(2)设ξ=x-y,求随机变量ξ的概率分布列与数学期望.

答案

(I)由题意知本题是一个等可能事件的概率,

试验发生包含的事件是从6张卡片中取2张,共有C62种结果,

满足条件的事件x、y同奇的取法有C32种,同偶的取法有C32

P=

2
C23
C26
=
2
5

(Ⅱ)由题意知变量ξ的可能取值是1,2,3,4,5,

P(ξ=1)=

5
C26
=
1
3
,P(ξ=2)=
4
C26
=
4
15
P(ξ=3)=
3
C26
=
1
5
,P(ξ=4)=
2
C26
=
2
15
,P(ξ=5)=
1
C26
=
1
15

其分布列为

ξ12345
P
1
3
4
15
1
5
2
15
1
15
Eξ=
5
15
×1+
4
15
×2+
3
15
×3+
2
15
×4+
1
15
×5=
7
3

完形填空
My neighbor’s children love playing hide-and-seek (捉迷藏) as all children do, but no one   36  that a game they played last week would be reported in the local newspaper.
One afternoon, they were playing in the vacant lot (空地)down by the corner. Young Paul, who is only five years old, found the perfect place to   37 . His sister, Natalie, had   38  her eyes and was counting to ten when Paul noticed the mail box at the corner and that the metal door was standing open. The mailman had just   39  several bags of mail and had carried them to his truck which was standing a few feet away. Paul climbed   40  the mail box and pulled the door closed so hard that it   41 . Soon realizing what he had done, he became   42  and started crying. At that time, Natalie was looking for him everywhere but could not find him. It was   43  that she happened to stand at the corner for a minute and heard her brother’s cries. She   44  ran to tell the mailman who hurried back from his   45  to unlock the metal door. Paul was now   46 , but he had such a bad fright that he could not stop crying. The mailman, however, soon found a way of making him   47  again. He told him that the next time he wanted to hide in a mail box, he should remember to put a stamp on himself!
小题1:
A.realizedB.warned C.imaginedD.wondered
小题2:
A.hideB.watch C.rest D.sleep
小题3:
A.openedB.shutC.raisedD.wiped
小题4:
A.lostB.foundC.taken outD.put in
小题5:
A.throughB.overC.out ofD.into
小题6:
A.brokeB.fell downC.openedD.locked
小题7:
A.surprisedB.frightenedC.excitedD.angry
小题8:
A.luckyB.a pityC.possibleD.strange
小题9:
A.suddenlyB.slowlyC.immediatelyD.carelessly
小题10:
A.homeB.truckC.mail boxD.post office
小题11:
A.foundB.hiddenC.happyD.free
小题12:
A.laughB.cryC.climb inD.play
多项选择题