You are in charge of quality control for a company manufactures a famous luxury brand of handbags. There are three different defects that you must be on the lookout for. A defect in any of these areas means the handbag can not be sold, and must be either recycled or destroyed.

• Defects in stitching: 11% of items
• Defects in coloring: 8% of items
• Defects in materials: 4% of items

Because the areas (stitching, coloring/dying, materials) are done by different suppliers or in different areas of the manufacturing plant, you may assume that the types of defects are independent of each other.

1. If there is a defect in all of the areas, the product must be destroyed. What percentage of bags will need to be destroyed?
2. A defect in coloring or materials means the product can not be recycled, and must therefore be destroyed. For what percentage of bags will this be the case?
3. What is the probability that a defect will be found of any of the three types?
4. What is the probability of finding at least one type of defect? (You must use the complement rule to answer this question.)