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A survey shows 34% of the respondents like soccer, 30% like tennis and 38% like
A survey shows 34% of the respondents like soccer, 30% like tennis and 38% like
游客
2025-02-23
10
管理
问题
A survey shows 34% of the respondents like soccer, 30% like tennis and 38% like baseball. 8% like both soccer and tennis, 10% like both tennis and baseball, and 5% like both soccer and baseball. If 3% respondents like all of them, then how many of respondents like none of them?
选项
A、15%
B、17%
C、18%
D、21%
E、82%
答案
C
解析
集合问题最常用的解题思想是画韦恩图求解。这道题目本质上是求喜欢三种球类中至少一种的人数百分比,即喜欢三种球类并集内的人数百分比。最后用1减去口述结果即可得答案。求喜欢三种球类并集内的人数百分比可以画出如下的韦恩图:
在画出图后,标清楚每一个最小单位的所占比例。例如上图中,中间的三者交集小圈为3%,T与S交集不包括中间小圈的部分为5%,B与S交集不包括中间小圈的部分为2%,T与B交集不包括中间小圈的部分为7%。S中未与其他任何运动相交的部分为34%-5%-3%-2%=24%,T中未与其他任何运动相交的部分为30%-7%-5%-3%=15%,B中未与其他任何运动相交的部分为38%-7%-2%-3%=26%。将每一个最小单位百分比相加即可得到喜欢三个球类的并集所占的百分比:24%+15%+26%+5%+3%+2%+7%=82%,1-82%=18%,故答案选C。
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