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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?

Please show your work.

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