There are three companies that produce a critical electronic navigation componen

Question

There are three companies that produce a critical electronic navigation component (ENC) used in the aerospace industry. These companies are Alice Manufacturing, Byte International, and Cognizant Technologies. Alice makes 85% of the ENCs, Byte makes 10%, and Cognizant makes the remaining 5%. The ENCs made by Alice have a 2.5% rate of defects, the ones made by Byte have a 4.0% rate of defects, and the ones made by Cognizant have a 6% rate of defects. If an ENC is randomly selected from the general population of ENCs, the probability that it was made by Alice is _______. If this ENC is later tested and found to be defective, the probability that it was made by Alice is _______.

Explanation / Answer

Probability that a randomly selected ENC from the general population of ENC's is made by Alice = 0.85

Probability that a randomly selected ENC is defective = 0.85*.025 + 0.10*0 04 + 0.05*0.06 = 0.02825

Now, probability that an ENC is made by Alice if it is found to be defective = (0.85*0.025)/0.02825 = 0.7522

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