问题 填空题

设正四面体ABCD的所有棱长都为1米,有一只蚂蚁从点A开始按以下规则前进:在每一个顶点处等可能的选择通过这个顶点的三条棱之一,并且沿着这条棱爬到尽头,则它爬了4米之后恰好位于顶点A的概率为______.

答案

由题意知本题是一个等可能事件的概率,

假设这个四面体的四个顶点分别为ABCD,蚂蚁从A开始爬.

如果爬到第三次时,蚂蚁在A点,那么第四次就一定不在A点,

∴设蚂蚁第三次在A点的概率为X,那么最后的答案就是

(1-X)
3

设蚂蚁第二次在A点的概率为Y,那么最后的概率就是X=

1-Y
3
    ②

显然蚂蚁第一次爬完之后在A点的概率为0,那么 Y=

1-0
3

将③代入②,得X=

1-
1
3
3
=
2
9

将④代入①得P=

1-
2
9
3
=
7
27

故答案为:

7
27

完形填空
When I was young, I always helped my grandfather in the fields. As I worked beside him, he        to tell a story about a man named Joe, and his wife, who moved to a new farm with their three sons. They were setting into the new place        a nearby farmer told Joe that there was gold in the earth. Joe was very       , and told his sons about it.
They began to dig in one corner, and they got to the end of the field. At the same time, Joe thought he would        some crops where the earth had been       . The plants included corn, tomatoes, potatoes, etc. His sons continued to dig through the soil, made up their mind to find the gold. Since        soil was being turned, Joe could plant more crops. Joe had never farmed before, but it had always been his       .
As different crops came ready to be harvested, Joe started to        that there were more vegetables than he and his family could ever       . One of Joe’s neighbors suggested that he        a vegetable shop. Joe and his wife did that very thing. They called it Joe and Family Vegetable. Joe even had to leave some crops in the fields,        he had more than enough to supply the vegetable shop.
This went on for years, and Joe and his wife became quite        from their little vegetable shop. They were even able to        their sons to college.
Remember the beginning of the story, when Joe was told by his new neighbor that there was gold in the land? Well, the truth is, Joe’s       of the English language was less than perfect. His new neighbor friend actually meant that his land had rich       . So you can see where the concept(概念)of gold comes from.
小题1:
A.fearedB.agreedC.usedD.failed
小题2:
A.whileB.asC.whenD.after
小题3:
A.happyB.disappointedC.angryD.calm
小题4:
A.harvestB.plantC.waterD.feed
小题5:
A.controlledB.burnedC.destroyedD.turned
小题6:
A.moreB.mostC.muchD.few
小题7:
A.jobB.problemC.pityD.dream
小题8:
A.realizeB.promiseC.reviewD.reply
小题9:
A.feedB.sellC.plantD.eat
小题10:
A.take upB.set upC.turn upD.make up
小题11:
A.nowB.thoughC.soD.because
小题12:
A.carefulB.richC.aloneD.cheerful
小题13:
A.bringB.takeC.sendD.make
小题14:
A.understandinB.knowledgeC.thinkingD.skills
小题15:
A.mudB.goldC.soilD.material
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