问题 解答题

一个不透明的布袋里装有4个大小、质地均相同的乒乓球,每个球上面分别标有1,2,3,4.小林先从布袋中随机抽取一个乒乓球(不放回去),再从剩下的3个球中随机抽取第二个乒乓球,记两次取得乒乓球上的数字依次为a、b.

(1)求a、b之积为偶数的概率;

(2)若c=5,求长为a、b、c的三条线段能围成三角形的概率.

答案

(1)根据题意列表如下:

由以上表格可知:有12种可能结果,分别为:(1,2),(1,3),(1,4),(2,1),(2,3),(2,4),

(3,1),(3,2),(3,4),(4,1),(4,2),(4,3),

其积分别为:2,3,4,2,6,8,3,6,12,4,8,12;

积为偶数的有2,4,2,6,8,6,12,4,8,12,共10个,

则P(数字之积为偶数)=

10
12
=
5
6

(2)所有的可能结果有12种,a,b及c的值分别为(1,2,5),(1,3,5),(1,4,5),(2,1,5),(2,3,5),(2,4,5),(3,1,5),(3,2,5),(3,4,5),(4,1,5),(4,2,5),(4,3,5),

能构成三角形的有(2,4,5),(3,4,5),(4,2,5),(4,3,5),共4种,

则P(三线段能围成三角形)=

4
12
=
1
3

阅读理解

Do you know why you sleep? You may think it’s because you’re tired. Or perhaps you’ve been told sleep is good for you. Yet no one knows exactly why or how people sleep.

Until the early 1950s, most scientists thought the body and brain rested during sleep. Then a scientist watched people sleep. He noticed that during periods of between 5 and 30 minutes each, sleepers’ eyes made rapid movements, as if they were watching something. He called these periods REM sleep, for Rapid Eye Movement. Periods when sleepers’ eyes did not move he called non-REM sleep.

Whenever the scientist woke people during REM sleep, they were having vivid dreams. Measurements showed that sleepers’ pulses(脉搏)went up quickly during REM sleep. Their breathing, heartbeat, and the blood going to the brain also increased. Far from being a time of rest, REM sleep is a time when the body is hard at work. Scientists still don’t know the reason for this. Some believe REM sleep makes learning easier. Babies spend a lot of time in REM sleep. Because of this, some scientists believe that REM sleep helps the brain grow. Others think REM sleep is a time for the brain to empty the day’s garbage.

One thing all the scientists agree on is that sleep is necessary. Without enough sleep, people make mistakes. Most major car accidents happen during the early morning hours, when people are sleepiest.

小题1:During REM sleep, a person’s breathing and heartbeat ________.

A.stop

B.increase

C.decrease

D.stay the same小题2:Which word in paragraph(段落)3 means “colorful and lively”?

A.easier

B.empty

C.vivid

D.quickly小题3:Which paragraph tells what happens when people don’t get enough sleep?

A.1

B.2

C.3

D.4小题4:What is the main idea of the article?

A.REM sleep helps the brain grow.

B.REM sleep has been watched and recorded by scientists.

C.REM sleep is a time to empty the day’s garbage.

D.REM sleep is an active time when the body is hard at work.小题5:You can decide from the article that REM sleep ________.

A.has a restful effect on people

B.can be avoided with lots of sleep

C.is something that all people experience

D.is something that all scientists agree on

填空题