Machine X produces 3% defectives, machine Y produces 4 % defectives, and machine Z produces 6% defectives. Of the total output from these machines, 50% of the items are from machine X, 30% from Y, and 20% from Z. One item is selected at random from a day’s production. 

A) What is the prior probability that the item came from machine Z? 

B) If the inspection finds the item to be defective, what is the revised probability that the item came from machine Z?

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