Three manufacturers supply door frames to a constructor of apartment complexes. The constructor, after years of testing door frames for fit and function, recorded the fraction of defective frames supplied by each manufacturer:

Manufacturer 1: 0.0
Manufacturer 2: 1/5
Manufacturer 3: 3/5
The constructor has ceased testing due to costs, assuming the fraction defective and inventory mix remain consistent. The project engineer randomly selects a door frame (with no identifying labels as to the supplier), tests it, and discovers it to be defective. Let A be the event that a frame is defective, and Bi be the event that the item came from supplier i (where i = 1, 2, 3). Use Bayes' Theorem to compute the probability that the defective frame was supplied by Manufacturer B (P(B|A)).

Hint: {B1, B2, B3} forms a partition.