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數(shù)學(xué)機(jī)經(jīng)

1. A box contains 100 balls, numbered from 1 to 100.If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?

A. 1/4

B. 3/8

C. 1/2

D. 5/8

E. 3/4

答案：C

解析：本題因?yàn)槠鏀?shù)和偶數(shù)個(gè)數(shù)相同，和也叧有兩種方式，所以三個(gè)數(shù)的和為奇數(shù)的可能性為1/2。也可以考慮從這100個(gè)數(shù)中獲取三個(gè)數(shù)的奇偶，可能性為：奇奇奇，奇偶偶，奇奇偶和偶偶偶，其中奇奇奇和奇偶偶兩種情況的和為奇數(shù)，所以也得到可能性為1/2

2. There are 1200 respondents to a poll, each favoring their preference for candidates A,B,and C.54% favored A,48% favored B,and 42% favored C,and there is 30% favored both A and B.What\'s the largest possible number of respondents favoring C,but not C&B,nor C&A?

A. 25%

B. 30%

C. 28%

D. 38%

E. 40%

答案：C

解析：A和B的并集為：54%+48%-30%=72%，所C為 28%

3. In an insurance company, each policy has a paper record and an electric record.For those policies having incorrect paper record,60% also having incorrect electric record;For policies having incorrect electric record,75% also having incorrect paper record.3% of all policies have both incorrect paper and incorrect electric records.If we randomly pick out one policy,what\'s the probability that the one having both correct paper and correct electric records?

A. 0.80

B. 0.94

C. 0.75

D. 0.88

E. 0.92

答案：B

解析：設(shè)總數(shù)為 x設(shè)incorrect paper record有y, incorrect electric record 有z，則：x·y·60%=3%·x y=5% x·z·75%=3%·x z=4%則，兩者至少有一個(gè)錯(cuò)誤的百分比為 5%+4%-3%=6%，所正確答案為 94%

4. If Bob can do a job in 20 days and Jane can do the job in 30 days, they work together to do this job and in this period,Bob stop work for 2.5 days and Jane stop work for x days, and the job be finished for 14 days, what is x?

A. 1.6

B. 3.2

C. 1.5

D. 1.25

E. 1.15

答案：D

解析：1/20(14-2.5)+1/30(14-x)=1，得出 x=1.25

5. The probability of A is 60% and the probability of B is 50%,what is the most possible probability that neither A nor B would happen?

A. 0.80

B. 0.40

C. 0.75

D. 0.55

E. 0.68

答案：B

解析：劃出圖表來(lái)可以一目了然：A， B 均丌發(fā)生癿最大概率為 40%，最小概率為0.因此選 B

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