A worker at an automobile plant is responsible for cleaning a CNC machine at the start of every shift. The probability that the machine has an operating failure during a random shift is 2% if it is cleaned and 10% if it is not cleaned. Suppose the worker can be relied on to clean the machine on 95% of shifts. (a) What is the probability that the CNC machine has an operating failure during a random shift? (b) If the machine has an operating failure during a shift, what is the probability that the worker did not clean it?

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