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题库 / GMATAdvanced-DS-9
Let S be a set of outcomes and let A and B be events with outcomes in S. Let ~B denote the set of all outcomes in S that are not in B and let P(A) denote the probability that event A occurs. What is the value of P(A)?
(1)P(A∪B)=0.7
(2)P(A∪~B)=0.9
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
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从哪里知道A B 是S的 所有Outcomes呢？
不能知道。所以条件1说，A并B是0.7，这说明还有outcomes不是A也不是B的。
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let A(only) + B(only) + AB(only) + neither = 1
from statement (1), it is clearly insufficient but it it means that neither = 0.3
from statement (2), it is clearly insufficient but it it means that B(only) = 0.1
by combining them, P(A) = A(only) + AB(only) = 1- (0.1+0.3) = 0.6
用韦恩图
P(A∪B) = P(A) + P(B) - P(AB)
P(A∪~B) = 1 - P(B) + P(AB)
那～B中是否包含P（A）的情况呢？
包括~
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求问为什么不考虑AB相交呢，如果相交，1+2求出p（A）=0.7啊
画韦恩图。a+b+d+n=1,求a+d？
(1)a+d+b=0.7，得n=0.3
(2)a+d+n=0.9
(1) (2)联立得a+d=0.6
P(A∪B) = P(A) + P(B) - P(AB)
P(A∪~B) = 1 - P(B) + P(AB)