# Poor quality candy

## Question

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.