1. **Problem:** Calculate the probability that a randomly selected item from the factory is defective given the production proportions and defect rates of machines A, B, and C. 2. **Formula:** Use the law of total probability: $$P(\text{Defective}) = P(A)P(\text{Defective}|A) + P(B)P(\text{Defective}|B) + P(C)P(\text{Defective}|C)$$ 3. **Given data:** - $P(A) = 0.50$, $P(\text{Defective}|A) = 0.04$ - $P(B) = 0.30$, $P(\text{Defective}|B) = 0.06$ - $P(C) = 0.20$, $P(\text{Defective}|C) = 0.10$ 4. **Calculation:** $$P(\text{Defective}) = (0.50)(0.04) + (0.30)(0.06) + (0.20)(0.10)$$ $$= 0.02 + 0.018 + 0.02$$ $$= 0.058$$ 5. **Interpretation:** The probability that a randomly selected item is defective is $0.058$, or 5.8%.