Given that \(P(A)=0.60, P(B)=0.40\), and \(P(A \cap B)=\) 0.24 , verify that

(a) \(P(A \mid B)=P(A)\);

(b) \(P(A \mid \bar{B})=P(A)\);

(c) \(P(B \mid A)=P(B)\);

(d) \(P(B \mid \bar{A})=P(B)\).