GMAT Focus EditionQuantitative ReasoningMedium
A quality control manager finds that 15% of the products manufactured by Machine A are defective, and 10% of the products manufactured by Machine B are defective. If 60% of the total production comes from Machine A and the rest from Machine B, what is the overall percentage of defective products?
- A13.5%
- B12.5%
- C13.0%
- D12.0%
Show answer & explanationAnswer & explanation
Correct answer: C. 13.0%
Let P(A) = 0.60 (production from Machine A) and P(B) = 0.40 (production from Machine B, since 1 - 0.60 = 0.40). Let P(Defective|A) = 0.15 and P(Defective|B) = 0.10. The overall percentage of defective products is P(Defective) = P(Defective|A) * P(A) + P(Defective|B) * P(B) = (0.15 * 0.60) + (0.10 * 0.40) = 0.09 + 0.04 = 0.13, or 13%.
Why the other options are wrong
- A. This is incorrect; it might be a miscalculation or an incorrect weighted average.
- B. This is incorrect; it might be a miscalculation or an incorrect weighted average.
- D. This is incorrect; it might be a miscalculation or an incorrect weighted average.
Weighted Average (Probability/Mixtures)
An average that takes into account the relative importance or frequency (weights) of each value in the data set.
- Each value is multiplied by its corresponding weight.
- The sum of these products is divided by the sum of the weights.
- Often used in probability (total probability), finance, and mixtures.
Memory trick: Weight times value, sum them all, then divide by total weight's call.