6. A retailer receives 75% of its batteries from Factory A and 25% from Factory B. The...

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6. A retailer receives 75% of its batteries from Factory A and 25% from Factory B. The percentages of defectives produced by A and B are known to be 1% and 2%, respectively.A customer has just bought a battery randomly from the retailer.

(a) What is the probability that the battery is defective?

(b) If the battery you bought is defective, what is the probability that it came from Factory A? (Hint: Use Bayes' theorem in Problem 5.)

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