A company has two machines, M1 and M2, producing widgets. M1 produces 60% of the widgets and M2 produces 40%. 3% of M1's widgets are defective, and 5% of M2's widgets are defective. If a randomly selected widget is found to be defective, what is the probability it came from M1?
Show answer & explanation
Correct answer: B
Explanation
Production from M1 = 60% = 0.6
Production from M2 = 40% = 0.4
Defective items from M1 = 3% = 0.03
Defective items from M2 = 5% = 0.05
= [P(M1) × P(Defective | M1)] ÷ Total defective
= (0.6 × 0.03) ÷ [(0.6 × 0.03) + (0.4 × 0.05)]
= 0.018 ÷ 0.038
≈ 0.47