There are 5% defective parts manufactured by your production line, and you would like to find these before they are shipped. A quick and inexpensive inspection method has been devised that identifies 8% of parts as defective. Of parts identified as defective, 50% are truly defective.
a. Complete a probability tree for this situation.
b. Find the probability that a defective part will be identified (i.e., the conditional probability of being identified given that the part was defective).
c. Find the probability that a part is defective or is identified as being defective.
d. Are the events “identified” and “defective” independent? How do you know?
e. Could an inspection method be useful if the events “identified” and “defective” were independent? Please explain.