Inventory for a manufacturer are produced at three different
plants, 45% from plant 1, 30% from plant 2, and 25% from plant
3. In addition, each plant produces at different levels of
quality. Plant 1 produces 2% defectives, plant 2 produces 5%
defectives, and plant 3 produces 8% defectives. a. What is the
probability that an item is defective? b. If an item from the
inventory is found to be defective, what is the probability that is
was produced in plant 2?