A and B are two events of a random experiment such that $P(B)=0.4$, $P(A \cap \bar{B}) = 0.5$, $P(A \cup B) + P(A|B) = 1.15$, then $P(A)=$
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Probability problems often involve a system of equations based on standard formulas: $P(A \cup B)=P(A)+P(B)-P(A\cap B)$, $P(A|B)=P(A\cap B)/P(B)$, and $P(A \cap \bar{B}) = P(A) - P(A \cap B)$. Write down all relationships first and substitute to solve for the unknown.