A company that produces a particular machine component has 3 factories, one each

Question

A company that produces a particular machine component has 3 factories, one each in Detroit, Pittsburgh, and Cleveland. 34% of the components produced come from the Detroit factory, 41% of the components come from the Pittsburgh factory, and 25% of the components come from the Cleveland factory. It is known that 1.8% of the components from the Detroit factory, 2.5% of the components from the Pittsburgh factory, and 2.9% of the components from the Cleveland factory are defective . Given that a component is selected at random and is found to be defective, what is the probability that the component was made in Cleveland?

Explanation / Answer

P(Detroit) = 0.34

P(Pittsburgh) = 0.41

P(Cleveland) = 0.25

P(Defective | Detroit) = 0.018

P(Defective | Pittsburgh) = 0.025

P(Defective | Cleveland) = 0.029

P(Defective) = P(Defective | Detroit) * P(Detroit) + P(Defective | Pittsburgh) * P(Pittsburgh) + P(Defective | Cleveland) * P(Cleveland)

                     = 0.018 * 0.34 + 0.025 * 0.41 + 0.029 * 0.25

                     = 0.02362

P(Cleveland | defective) = P(Defective | Cleveland) * P(Cleveland) / P(defective)

                                       = 0.029 * 0.25 / 0.02362

                                       = 0.3069

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.