In a factory there are three types of machines M1, M2 and M3 which produce 25%, 35% and 40% of the total output respectively. Machines M1, M2 and M3 produce 2%, 4% and 5% defective products respectively. What percentage of the total products manufactured by the factory are non-defective?

Introduction / Context:
This question is about weighted probabilities and percentages. Each machine contributes a different share of the total production and also has its own defective rate. To find the overall percentage of non defective items, you must weight each machine defect rate by its share in the total production and subtract the resulting overall defect rate from 100%.

Given Data / Assumptions:

Machine M1 produces 25% of the total products and 2% of these are defective.

Machine M2 produces 35% of the total products and 4% of these are defective.

Machine M3 produces 40% of the total products and 5% of these are defective.

We assume that all products come from these three machines only.

Concept / Approach:
The overall defective percentage is the sum of the defective contributions from each machine. For each machine, we multiply its share of total production by its defect rate. The overall non defective percentage is then 100% minus the overall defective percentage. This is a classic application of the law of total probability in percentage form.

Step-by-Step Solution:
Step 1: Consider total production as 100 units for easy calculation.Step 2: Units produced by M1 = 25% of 100 = 25 units.Step 3: Units produced by M2 = 35% of 100 = 35 units.Step 4: Units produced by M3 = 40% of 100 = 40 units.Step 5: Defective units from M1 = 2% of 25 = (2 / 100) * 25 = 0.5 units.Step 6: Defective units from M2 = 4% of 35 = (4 / 100) * 35 = 1.4 units.Step 7: Defective units from M3 = 5% of 40 = (5 / 100) * 40 = 2 units.Step 8: Total defective units = 0.5 + 1.4 + 2 = 3.9 units out of 100.Step 9: Overall defective percentage = 3.9%.Step 10: Overall non defective percentage = 100% − 3.9% = 96.1%.

Verification / Alternative check:
Instead of working with units, work directly with percentages. Contribution to defect rate from M1 = 0.25 * 2% = 0.5%. From M2 = 0.35 * 4% = 1.4%. From M3 = 0.40 * 5% = 2%. Sum = 0.5% + 1.4% + 2% = 3.9%. Non defective percentage = 100% − 3.9% = 96.1%. Both methods are identical and confirm the answer.

Why Other Options Are Wrong:
89% and 86.1% are much too low and would correspond to a much higher overall defect rate than the data support.
97.1% is slightly higher than the correct 96.1% and does not match the summed contributions of the three machines.
92.9% is another distractor value and does not arise from any correct weighting calculation.

Common Pitfalls:
Some students incorrectly average the defect rates 2%, 4% and 5% without weighting by production share, which ignores the fact that M3 produces more items. Others mistakenly add the production percentages before multiplying by defect percentages. Always remember to multiply each machine share by its own defect rate and then add these contributions to find the overall defect rate.

Final Answer:
The percentage of non defective products manufactured by the factory is 96.1%.