The Johnson Company receives connector rods from three different producers. We w

Question

The Johnson Company receives connector rods from three different producers. We will call them Company A, Company B and Company C. As the quality control inspector you check the rods as they come in. From past experience you know that 12% of the rods from Company A are faulty, 8% of the rods from Company B are faulty and 9% of the rods from Company C are faulty. 40% of the rods come from Company A, 30% come from Company B and 30% come from Company C. You randomly pick a connector rod and find out that it is faulty. What is the probability that it came from Company C?

Explanation / Answer

Suppose Total rods = 100x

Rods from Company A =40% of 100x = 40x

Rods from Company B = 30% of 100x = 30x

Rods from Company C = 30% of 100x = 30x

Now

faulty rods from Company A = 12% of 40x = 4.8x

Faulty rods from Company B = 8% of 30x = 2.4x

Faulty rods from Company C = 9% of 30x = 2.7x

Total faulty rods = 4.8x +2.4x +2.7x = 9.9x

Probability (faulty rods from Company C )

= number of faulty rods from Company C / Total number of faulty roads

= 2.7x / 9.9 x

= 27/99

= 3/11

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