The certain item is manufactured by three factories, say 1, 2 and 3. It is known that 1 turns out twice as many items as 2 and that 2 and 3 turn out the same number of items (during a specified production period). It is also known that 2 percent of the items produced by 1 and 2 are defective while 4 percent of those manufactured by 3 are defective. All the items produced are put into one stock pile and then one item is chosen at random. The chosen item was found defective. What is the probability that it was produced in factory 1?
This is a problem of Bayes' theorem. ### Step 1: Define Events Let: - \( A_1 \), \( A_2 \), and \( A_3 \) be the events that the chosen item was produced by factory 1, 2, or 3, respectively. - \( B \) be the event that the chosen ____ ________ _______ ________ ____ _______ ____ __________.
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The certain item is manufactured by three factories, say 1, 2 and 3. It is known that 1 turns out twice as many items as 2 and that 2 and 3 turn out the same number of items (during a specified production period). It is also known that 2 percent of the items produced by 1 and 2 are defective while 4 percent of those manufactured by 3 are defective. All the items produced are put into one stock pile and then one item is chosen at random. The chosen item was found defective. What is the probability that it was produced in factory 1?
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