Three plants manufacture hard drives and ship them to a warehouse for distribution. Plant I produces 54% of the warehouse’s inventory with a 4% defect rate. Plant II produces 35% of the warehouse’s inventory with an 8% defect rate. Plant III produces the remainder of the warehouse’s inventory with a 12% defect rate. 

a. Draw a tree diagram to represent this information.
b. A warehouse inspector selects one hard drive at random. What is the probability that it is a defective hard drive and from Plant II?