Question

Inspecting final products.

final products are sometimes selected to go through a complete inspection before leaving the production facility.
suppose that 8% of all products made at a particular facility fail to conformto specifications.
furthermore, 55% of all nonconforming items are selected for complete inspection while 20% of all conforming items are selected for complete inspection.
given that a randomly chosen item has gone through a complete inspection, what is the probability the item is nonconforming?

Answer 1

P(non-conforming and complete inspection) = 0.08 x 0.55 = 0.044
P(conforming and complete inspection) - 0.92 x 0.2 = 0.184
P(complete inspection) = 0.044 + 0.184 = 0.228
P(non-conforming|complete inspection) = 0.044/0.228 = 0.193

the answer is 0.193 or 19.3%