Before leaving the factory, items are inspected to determine if they are good for use or defective (defective no or yes). Suppose 10 percent of items actually are flawed. If an item is flawed, the inspection process will label it as negative (-) with probability 0.9 (negative yes or no). If the item is not flawed, the inspection process will label it negative (-) with probability 0.05. Let F denote the event the item is flawed, and − denote the event the item is labeled as negative. So we have F for flawed and F c for not flawed, and − for negative and −c (or +) for not negative (positive). a. What is the probability a randomly chosen item is labeled negative -? b. An item is labeled negative -. What is the probability that the item is flawed (given it is labeled negative)
Before leaving the factory, items are inspected to determine if they are good for use or defective (defective no or yes). Suppose 10 percent of items actually are flawed. If an item is flawed, the inspection process will label it as negative (-) with
a. What is the probability a randomly chosen item is labeled negative -?
b. An item is labeled negative -. What is the probability that the item is flawed (given it is labeled negative)
c. Are the events F and − independent? Why or why not.
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