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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Since \(P(A) = a = 1 – ( c + d ) – 0.25 = 0.75 – (c + d)\), then \(P(A)\) can be determined from the value of \(c + d\). Thus, the answer is \(B\).

Condition 1)

If \(P(A) = 0.5, P(B) = 0.25\) and \(P(C) = 0\), then we have \(P(A) = 0.5.\)

If \(P(A) = 0.4, P(B) = 0.25\) and \(P(C) = 0.1\), then we have \(P(A) = 0.4.\)

Thus, condition 1) is not sufficient.

Condition 2)

Since \(P(A) + P(B) + P(C) + P(D) = 1, P(B) = 0.25\) and \(P(C) + P(D) = 0.25\) from condition 2), we have \(P(A) = 0.5.\)

Thus, condition 2) is sufficient.

Therefore, the answer is B.

Answer: B

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