(A)=0.6, (B)=0.4, (B|overline (A))=0.5，则(A)=0.6, (B)=0.4, (B|overline (A))=0.5，(A)=0.6, (B)=0.4, (B|overline (A))=0.5

步骤 1：计算$P(\overline{A})$
$P(\overline{A}) = 1 - P(A) = 1 - 0.6 = 0.4$

步骤 2：计算$P(\overline{B})$
$P(\overline{B}) = 1 - P(B) = 1 - 0.4 = 0.6$

步骤 3：计算$P(B|\overline{A})$
已知$P(B|\overline{A}) = 0.5$

步骤 4：计算$P(\overline{A} \cap B)$
$P(\overline{A} \cap B) = P(B|\overline{A}) \cdot P(\overline{A}) = 0.5 \cdot 0.4 = 0.2$

步骤 5：计算$P(A \cap \overline{B})$
$P(A \cap \overline{B}) = P(A) - P(A \cap B)$
$P(A \cap B) = P(A) + P(B) - P(A \cup B)$
$P(A \cup B) = P(A) + P(B) - P(A \cap B)$
$P(A \cap B) = P(A) + P(B) - P(A \cup B)$
$P(A \cap B) = 0.6 + 0.4 - P(A \cup B)$
$P(A \cap B) = 1 - P(A \cup B)$
$P(A \cap \overline{B}) = P(A) - (1 - P(A \cup B))$
$P(A \cap \overline{B}) = 0.6 - (1 - P(A \cup B))$
$P(A \cap \overline{B}) = P(A \cup B) - 0.4$

步骤 6：计算$P(A|\overline{B})$
$P(A|\overline{B}) = \frac{P(A \cap \overline{B})}{P(\overline{B})} = \frac{P(A \cup B) - 0.4}{0.6}$

步骤 7：计算$P(A \cup B)$
$P(A \cup B) = P(A) + P(B) - P(A \cap B)$
$P(A \cup B) = 0.6 + 0.4 - P(A \cap B)$
$P(A \cup B) = 1 - P(A \cap B)$
$P(A \cap B) = P(A) + P(B) - P(A \cup B)$
$P(A \cap B) = 0.6 + 0.4 - P(A \cup B)$
$P(A \cap B) = 1 - P(A \cup B)$
$P(A \cup B) = 1 - P(A \cap B)$
$P(A \cup B) = 1 - (0.6 + 0.4 - P(A \cup B))$
$P(A \cup B) = 1 - 1 + P(A \cup B)$
$P(A \cup B) = P(A \cup B)$
$P(A \cup B) = 1$