87學測數學單選第3題詳解

依機率排容原理，$p = P(A \cup B) = P(A) + P(B) - P(A \cap B) = \dfrac{1}{2} + \dfrac{1}{3} - P(A \cap B) = \dfrac{5}{6} - P(A \cap B)$。因為 $0 \le P(A \cap B) \le P(B) = \dfrac{1}{3}$，所以可得 $$\dfrac{5}{6} - \dfrac{1}{3} \le p \le \dfrac{5}{6} - 0 \implies \dfrac{1}{2} \le p \le \dfrac{5}{6}$$ 故選 $(4)$。