A manufacturing firm gets its parts from one of two firms: Firm A and Firm B. Ov

Question

A manufacturing firm gets its parts from one of two firms: Firm A and Firm B. Overall, 80% of its parts come from Firm A, and the rest come from Firm A.

The quality level, however, differs between suppliers: 98% of the parts received from Firm A are ‘high quality’ (the rest are ‘low quality’), while only 90% of the parts received from Firm B are ‘high quality’ (again, the rest are ‘low quality’).

Today, a low quality part has broken one of your machines. What is the probability the part came from Firm A? What is the probability it came from Firm B?

Explanation / Answer

P(low quality) = P(Firm A)*P(low quality | Firm A) + P(Firm B)*P(low quality | Firm B)

= 80% * 2% + 20% * 10% = 3.6%

P(Firm A | low quality) = P(Firm A)*P(low quality | Firm A) / P(low quality) = 80% * 2% / 3.6% = 44.44%

Answer: 44.44%

P(Firm B | low quality) = 1-P(Firm A | low quality) = (100-44.44)% = 55.56%

Answer: 55.56%

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