Question

A garment manufacturer in Bangladesh has three plants named A, B, and C. Plant A produces 40% of the clothing, plant B produces 30%, and plant C produces 30%. The plants A, B, and C have 5%, 4%, and 3% defect rate for their production. A quality control manager has just found a defective garment item and he wants to find out which plant is more likely to have produced the defective item. Answer the following questions to mathematically derive a conclusion on the plant that has produced the faulty item. Let's define the following events: A is the event that plant A produces the item B is the event that plant B produces the item C is the event that plant C produces the item D is the event that a product is defective. Find the P(D|A): Find the P(D|B): Find the P(D|C): Find the P(A∩D): Find the P(D):

Find the P(A|D):Find the P(B|D):Find the P(C|D):

Answer 1

The following probabilities are defined.

. The event

The given conditional probabilities are

Using total probability theorem,

The conditional probabilities,