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题目

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：本题因为奇数和偶数个数相同，和也只有两种方式，所以三个数的和为奇数的可能性为1/2。也可以考虑从这100个数中任取三个数的奇偶，可能性为：奇奇奇，奇偶偶，奇奇偶和偶偶偶，其中奇奇奇和奇偶偶两种情况的和为奇数，所以也得到可能性为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. Whats the largest possible number of respondents favoring C, but not CB, nor CA?

A. 25%

B. 30%

C. 28%

D. 38%

E. 40%

答案：C

解析：A和B的并集为：54%+48%-30%=72%，所C为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, whats 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：设总数为x，设incorrect paper record有y, incorrect electric record有z，则：

xy60%=3%x y=5%

xz75%=3%x z=4%

则，两者至少有一个错误的百分比为5%+4%-3%=6%，所正确答案为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：划出图表来可以一目了然：A， B均不发生的最大概率为40%，最小概率为0.因此选B

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