23Total probability, defective part

Machine 1 makes 60% of parts, 2% defective; machine 2 makes 40%, 5% defective. Find $\displaystyle P(\text{a random part is defective})$.

Split by which machine made the part: P(D) = P(M1)P(D|M1) + P(M2)P(D|M2) = 0.6(0.02) + 0.4(0.05) = 0.012 + 0.02 = 0.032. So about 3.2% of parts are defective.