Poor quality candy

A candy manufacturer has three locations producing boxes of its famous product. The Scranton plant produces 30% of the product, of which 0.5% are below the quality standard. The Los Angeles plant produces 50% of the boxes, of which 0.75% are below the quality standard. Lastly, the Detroit plant produces the remaining 20%, of which 0.25% are below the quality standard. If a box of the candy is purchased at a store and found to be below the expected quality, what is the probability that it was manufactured by the Detroit plant? This type of problem can be solved using Bayes’ theorem.