4. In a factory, three machines M1, M2, and M3 make 30%, 45%, and 25% of the sen

Question

4. In a factory, three machines M1, M2, and M3 make 30%, 45%, and 25% of the sensors, respectively. Past data shows that 2%, 3%, and 2% of sensors made by each machine are defective, respectively. a. If a sensor is randomly selected from the factory, what is the probability it is defective? b. If a randomly selected sensor is found to be defective, wh 4. In a factory, three machines M1, M2, and M3 make 30%, 45%, and 25% of the sensors, respectively. Past data shows that 2%, 3%, and 2% of sensors made by each machine are defective, respectively. a. If a sensor is randomly selected from the factory, what is the probability it is defective? b. If a randomly selected sensor is found to be defective, wh 4. In a factory, three machines M1, M2, and M3 make 30%, 45%, and 25% of the sensors, respectively. Past data shows that 2%, 3%, and 2% of sensors made by each machine are defective, respectively. a. If a sensor is randomly selected from the factory, what is the probability it is defective? b. If a randomly selected sensor is found to be defective, wh

Explanation / Answer

Ans:

Given that

P(M1)=0.30

P(M2)=0.45

P(M3)=0.25

P(defective/M1)=0.02

P(defective/M2)=0.03

P(defective/M3)=0.02

a)

P(defective)=P(defective/M1)*P(M1)+P(defective/M2)*P(M2)+P(defective/M3)*P(M3)

=0.02*0.30+0.03*0.45+0.02*0.25

=0.0245

b)

P(M1/defective)=P(defective/M1)*P(M1)/P(defective)=0.02*0.3/0.0245=0.245

P(M2/defective)=P(defective/M2)*P(M2)/P(defective)=0.03*0.45/0.0245=0.551

P(M3/defective)=P(defective/M3)*P(M3)/P(defective)=0.02*0.25/0.0245=0.204

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