【正确答案】 C

【答案解析】The general addition rule for sets applied to probability gives the basic probability equationP(A∪B) = P(A) + P(B) -P(A∩ B).(1) Given that P(A ∪ B) = 0.7, it is not possible to determine the value of P(A) because nothing is known about the relation of event A to event B. For example, if every outcome in event B is an outcome in event A, then A ∪ B = A and we have P{A ∪ B) = P(A) = 0.7. However, if events A and B are mutually exclusive (i.e., P(A ∩ B) = 0) and P{B} = 0.2, then the basic probability equation above becomes 0.7 = P(A) + 0.2 - 0, and we have P{A} = 0.5; NOT sufficient.(2) Given that P(A ∪ ~B) = 0.9, it is not possible to determine the value of P{A} because nothing is known about the relation of event A to event ~B. For example, as indicated in the first figure below, if every outcome in event ~B is an outcome in event A, then A ∪ ~B = A and we have P(A ∪ ~B) = P(A) = 0.9. However, as indicated in the second figure below, if events A and ~B are mutually exclusive (i.e., P(A ∩ ~B) = 0) and P(~B) = 0.2, then the basic probability equation above, with ~B in place of 5, becomes 0.9 = P{A} + 0.2 - 0, and we have P(A) = 0.7; NOT sufficient.Given (1) and (2), if we can express events as a union or intersection of events A ∪ B and A ∪ ~B, then the basic probability equation above can be used to determine the value of P{A}.The figure below shows Venn diagram representations of events A ∪ B and A ∪ ~B by the shading of appropriate regions.