A manufacturing firm gets its parts from one of two firms Fi

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?

Solution

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%