www 8A Company buy fires from two suppliers 1 and 2 Supplier

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(8)A Company buy fires from two suppliers 1 and 2. Supplier 1 has a record of delivering tires that contain 10% defective, whereas supplier 2 has a defective rate of only 5%. Suppose that 30% of the current supply came from supplier 1. If a tire taken at random from this supply is observed to be defective, what is the probability that it came from supplier 2?

Solution

first, if 30% came from supplier 1, then 70% (1 - .3) come from supplier 2.

P(Tire is defective) = P(tire came from supplier 1)*P(Defective given tire came from supplier 1) + P(tire came from supplier 2)*P(defective given tire came from supplier 2)

P(tire is defective) = .3*.10 + .7*.05

P(tire is defective) = 0.065

P(tire is from supplier 2 given tire is defective) = P(tire is from supplier 2)*P(defective given tire is from supplier 2)/P(tire is defective)

P(tire is from supplier 2 given tire is defective) = .7*.05/.065 = 0.5385 (answer)