4. An aircraft emergency locator transmitter (ELT) is a device designed to trans

Question

4. An aircraft emergency locator transmitter (ELT) is a device designed to transmit a signal in the case of crash. The Alpha Manufacturing Company makes 70% of the ELTs, the Beta Company makes 20% of them, and the Gamma Company makes the other 10%. The ELTs made by Alpha have a 4% rate of defects, the Beta ELTs have a 6% rate of defects, and the Gamma ELTs have a 2% rate of defects. (a) If an ELT is randomly selected from the general population of all ELTs, what is the probability that it is defected. (b) If a randomly selected ELT is then tested and is found to be defective, find the probability that it was made by the Beta Manufacturing Company

Explanation / Answer

a)P(defected)=P(alpha and defected+beta and defected+gamma and defected)

=0.7*0.04+0.2*0.06+0.1*0.02 =0.042

b) P(defective|beta company) =P(beta and defected)/P(defective) =0.2*0.06/0.042=0.2857

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