math
A company has two factories that manufacture tires. Suppose 65% of the tires are manufactured in factory 1 and 35% are manufactured in factory 2. In factory 1, 5% of the tires are defective. In factory 2, 2% of the tires are defective.
a) Determine the probability that a defective tire is produced
b) A defective tire is discovered. What is the probability the defective tire came from factory 2?
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Answers
a) The probability that a defective tire is produced is 0.07 (7%), calculated as follows: P(defective) = P(F1) * P(defective|F1) + P(F2) * P(defective|F2) = 0.65 * 0.05 + 0.35 * 0.02 = 0.07 b) The probability that the defective tire came from factory 2 is 0.21 (21%), calculated as follows: P(F2|defective) = P(defective|F2) * P(F2) / P(defective) = 0.02 * 0.35 / 0.07 = 0.21
