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A keyboard manufacturer has 3 factories: Factory A, Factory B, and Factory C. Factory A, Factory B, and Factory C manufacture 10%, 40%, and 50% of all the manufactured keyboards, respectively. 10% of the keyboards manufactured in Factory A are defective, 5% of the keyboards manufactured in Factory B are defective, and 1% of the keyboards manufactured in Factory C are defective. You bought a keyboard from this manufacturer, and it is defective.

(a) What is the probability that the keyboard you bought was manufactured in Factory A? Show your work.

(b) What is the probability that the keyboard you bought was manufactured in Factory A or Factory B? Show your work.

 

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