1. **Problem statement:** If two events A and B are mutually exclusive and $P(A) = 0.6$ and $P(A \cup B) = 0.8$, find $P(B)$. 2. **Formula and rules:** For mutually exclusive events, $P(A \cap B) = 0$. The formula for the union of two events is: $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$ Since $A$ and $B$ are mutually exclusive, this simplifies to: $$P(A \cup B) = P(A) + P(B)$$ 3. **Substitute known values:** $$0.8 = 0.6 + P(B)$$ 4. **Solve for $P(B)$:** $$P(B) = 0.8 - 0.6$$ $$P(B) = 0.2$$ 5. **Answer:** The probability of event B is $\boxed{0.2}$.