问题 解答题

今有标号为1,2,3,4,5的五封信,另有同样标号的五个信封.现将五封信任意地装入五个信封,每个信封装入一封信,试求至少有两封信配对的概率.

答案

设恰有两封信配对为事件A,

恰有三封信配对为事件B,

恰有四封信(也即五封信配对)为事件C,

则“至少有两封信配对”事件等于A+B+C,且A、B、C两两互斥.

∵P(A)=

C25
•2
A55
,P(B)=
C35
A55
,P(C)=
1
A55

∴所求概率P(A)+P(B)+P(C)=

31
120

答:至少有两封信配对的概率是

31
120

填空题
完形填空

完形填空(共20小题;每小题1.5分,满分30分)

阅读下面短文,掌握大意,然后从41-60各题所给的四个选项(A、B、C和D)中,选出最佳选项,并在答题卡上将该项涂黑。

At a young age, her doctor told Patti Wilson she was an epileptic(羊癫疯患者). Her father was a morning jogger. One day she   31   and said, “Daddy, what I’d really love to do is run with you every day, but I’m afraid I can’t do it.” Her father   32    her to start running.

That’s just what they did every   33  . It was a   34   experience for them. After a few weeks, Patti said, still smiling, “Daddy, what I’d really love to do is break the world’s long-distance running record for  35   .”

Her father   36    The Guinness Book of World Records and found that the farthest distance any woman had run was 80 miles. As a freshman(新生) in high school, Patti    37   , “I’m going to run from Orange County up to San Francisco(about 400 miles).” “As a sophomore(二年级学生),” she went   38   , “I’m going to run to Portland, Oregon(about 1,500 miles). As a junior I’ll run to St. Louis(about 2,000 miles). As a senior I’ll run to the White House (about 3,000 miles).”

In   39   of her disease, Patti was as ambitious(有野心的) as she was enthusiastic. She looked at being an epileptic as simply “an   40  ”. She focused not on what she had   41   , but on what she had left.

That year, together with her father, she completed her   42   to San Francisco wearing a T-shirt that   43  , “I love Epileptics.”

In her sophomore year, Patti’s classmates got behind her. They made a huge poster that read, “Run, Patti, Run!” This has since   44   her motto and the title of a book she has written. During this marathon, she broke a bone in her foot. A doctor told her that she had to   45     her run. But Patti said she wasn’t running for herself; she was   46   to break the chains on the brains that limited so many others. She asked the doctor   47    or not there was a way she could keep running. He said he could wrap it in adhesive(粘合剂)  48   putting it in a cast(石膏), but he   49   her that it would be extremely painful. She told the doctor to wrap it up.

Later, after four months of running from the West Coast to the East Coast, Patti arrived in Washington and shook the hand of the President of the United States. She told him, “I wanted people to know that epileptics are normal human beings with   50   lives.”

31. A. smiled  B. cried   C. laughed      D. wept

32. A. agreed  B. suggested   C. encouraged D. promised

33. A. afternoon     B. morning     C. night   D. evening

34. A. terrible B. fortunate    C. dangerous       D. wonderful

35. A. women B. men    C. students      D. patients

36. A. questioned   B. checked      C. inspected    D. interviewed

37.A. broadcasted   B. told    C. informed        D. announced

38. A. up B. forward      C. on      D. upon

39. A. honor B. view       C. favor  D. charge

40. A. accident       B. coincidence       C. influence    D. inconvenience

41. A. lost      B. dropped     C. improved   D. received

42. A. distance       B. task    C. run     D. study

43. A. showed B. said    C. wrote  D. read

44. A. come    B. become      C. gone       D. went

45. A. continue      B. stop    C. keep      D. struggle

46. A. working       B. jogging      C. walking   D. running

47. A. whether       B. when  C. if D. where

48. A. in addition to      B. in spite of   C. instead of   D. regardless of

49. A. asked    B. warned       C. advised      D. comforted

50. A. common      B. unique       C. special       D. normal