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A factory production line makes widgets using two machines, A and B. Of the total output,...

A factory production line makes widgets using two machines, A and B. Of the total output, machine A is responsible for 45%and machine B for 55%. It is known from previous experience with the machines that 5% of the output from machine A is defective and 2% from machine B is defective. A widget is chosen at random from the production line and found to be defective. What is the probability that it came from machine A. Give your answer to 3 decimal places.

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