Question: When a machine is properly calibrated, 0.5% of its output is defective, but when it is out of adjustment, 6% of the output is defective.

When a machine is properly calibrated, 0.5% of its output is defective, but when it is out of adjustment, 6% of the output is defective. The technician in charge of calibration can successfully calibrate the machine in 90% of his attempts. The technician has just made an attempt to calibrate the machine.
a. What is the probability that the machine is in adjustment?
b. The first unit produced after the calibration effort is found to be defective. Given this information, what is the probability that the machine is in adjustment?

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