Three events $A$, $B$, and $C$ are mutually exclusive and exhaustive. A student is analyzing an event $X$ defined on the same sample space. It is given that $P(X \mid A) = 0.2$, $P(X \mid B) = 0.6$, and $P(X \mid C) = 0.5$. If $P(A) = 0.3$, $P(B) = 0.3$, and $P(C) = 0.4$, find the probability of the complement $P(X^c)$.