[問題]集合

[Grace]

In a certain group, 40 percent of the people belong to club A, 50 percent of the people belong to club B, 60 percent of the people belong to club C, 10 percent of the people belong to all three clubs, and 30 percent of the people belong to only two of these three clubs. If there are 3256 people in this group, approzimately how many people belong to none of these three clubs?

A 64
B 32
c 16
D 8
E 0

Ans. E.

請幫忙解惑 Many thanks~

[Behemoth]

a---0.4
b---0.5
c---0.6

a+b=a+c=b+c=0.2 題目說的

設在三個club外的有x人

那麼根據集合公式

a+b+c-a且b-a且c-b且c+a且b且c+不屬於abc之外的=1

0.4+0.5+0.6-0.2-0.2-0.2+0.1+x=1

x=0

所以就e囉~

[吳志道]

按照 我對題目的了解

應該是 0.6+0.4+0.5 -0.3-0.3-0.3+0.1+x=1

不過這樣 x=0.3 迷答案

請教大大 我思路哪有問題 >"<~

[魚]

按照 我對題目的了解

應該是 0.6+0.4+0.5 -0.3-0.3-0.3+0.1+x=1

不過這樣 x=0.3 迷答案

請教大大 我思路哪有問題 >"<~

0.6+0.4+0.5 -0.3-0.3+0.1+x=1 X=0

i guess you misunderstanding this sentence :

and 30 percent of the people belong to only two of these three clubs.

according the above , A&B +A&C + B&C - A&B&C = 0.3 :)

[homaru]

我算
0.6+0.4+0.5-0.3-0.1-0.1+X=1
X=0

可以畫三個重疊圈圈表示
最中間的ABC交集為0.1(重疊3次,所以減掉兩次)
旁邊的三葉AB,BC,AC交集(不含ABC交集)共計0.3(重疊兩次,所以減掉一次)
有點抽象...

[吳志道]

我懂了^^"" 英文不夠好^^" 謝謝樓上兩位大大

我會幫你們念經禱告的 阿咪偷夫 ^Q^

[Behemoth]

按照 我對題目的了解

應該是 0.6+0.4+0.5 -0.3-0.3-0.3+0.1+x=1

不過這樣 x=0.3 迷答案

請教大大 我思路哪有問題 >"<~

吳大 你是對的

我題目看太快把0.3看成0.2

如果說原題30 percent of the people belong to only two of these three clubs已包含ab+bc+ac

那麼原式改為 0.6+0.4+0.5-0.3+0.1+x=1

x=-0.3

不管如何 我覺得題目很怪

[Grace]

感謝各位的指點...畫了圖後果然清楚多了..
總覺的這題在考英文理解阿....

大家加油囉 ~ :P

[Grace]

0.6+0.4+0.5 -0.3-0.3+0.1+x=1 X=0
i guess you misunderstanding this sentence :
and 30 percent of the people belong to only two of these three clubs.
according the above , A&B +A&C + B&C - A&B&C = 0.3


關於這題,我又有一個問題..
若題目是寫 30 percent of the people belong to only one of these three clubs.
那麼它的意思又為何呢??


ps. 我實在不是很理解這樣的表達方式 help~

[吳志道]

根據前兩位大大教導

(1)30 percent of the people belong to only two of these three clubs-->純粹 A^B B^C C^A (少了交集的部分)

(2)30 percent of the people belong to only one of these three clubs.
-->純粹 A B C 也是少了交集的部分
= 指參加一種有多少% 30乘3=90%

請指教^^