问题 解答题
现有一条长度为1的绳子.
(1)用剪刀剪成两段,使得两段长度都大于
1
3
的概率是多少?
(2)用剪刀剪成三段,使三段能构成三角形的概率是多少?
答案

(1)若想两段长短都大于

1
3
,则只能在两个三等分点之间剪断,则其概率为
1
3

(2)设三段长分别为x,y,1-x-y,

0<x<1
0<y<1
0<1-x-y<1
0<x<1
0<y<1
0<x+y<1
其区域构成三角形OAB(如图14-4-5).

若使剪成的三段构成三角形,则x,y须满足:

x+y>1-x-y
y+1-x-y>x
x+1-x-y>y
x+y>
1
2
0<x<
1
2
0<y<
1
2
此时的区域为三角形CDE,故所求概率为
1
4

阅读理解

阅读理解。

     In general, people talk about two groups of colors: warm colors and cool colors. Researchers in

psychology think that there are also two groups of people: people who prefer warm colors and people

who prefer cool colors.

    The warm colors are red, orange and yellow. Where there are warm colors and a lot of light, people

usually want to be active. People think that red, for example, is exciting. Sociable people, those who like

to be with others, like red. The cool colors are green, blue and violet. These colors, unlike warm colors,

are relaxing. Where there are cool colors, people are usually quiet. People who like to spend time alone

often prefer blue.

    Red may be exciting, but one researcher says that time seems to pass more slowly in a room with

warm colors than in a room with cool colors. He suggests that a warm color, such as red or orange is a

good color for a living room or restaurant. People who are talking or eating do not want time to pass

quickly. Cool colors are better for offices or factories if the people who are working there want time to

pass quickly.

    Researchers do not know why people think some colors are warm and other colors are cool.

However, almost everyone agrees that red, orange, and yellow are warm and that green, blue, and violet

are cool. Perhaps warm colors remind people of warm days and the cool colors remind them of cool

days. Because in the north the sun is higher during summer, the hot summer sunlight appears yellow. 

1. Which of the following colors belong to cool colors?  

A. Yellow, green.      

B. Blue, violet. 

C. Black, blue.        

D. Brown, white. 

2. Which of the following statements is not true?   

A. Sociable people like warm colors. 

B. Warm colors can make people excited. 

C. People who like to be with others don't like red. 

D. Where there are warm colors, people want to be active. 

3. Which is the right color for different rooms?    

A. Red or orange for offices.  

B. Orange for dining-rooms. 

C. Blue for bedrooms.      

D. Red for studies. 

4. What is the main idea of the last paragraph? 

A. It shows the reason why people think some colors are warm and others are cool. 

B. Warm colors remind people of warm days.

C. Cool colors remind people of cool days.

D. People have an agreeable opinion of warm colors and cool colors.

多项选择题