A survey of workers in the two plants of a manufacturing firm includes the question “How effective is management in responding to legitimate grievances of workers?” In plant 1, 48 of 192 workers respond “poor”; in plant 2, 80 of 248 workers respond “poor”. An employee of the manufacturing firm is to be selected randomly. Let A be the event “worker comes from plant 1” and let B be the event “response is ‘poor’.” Find P(A), P(B), and P(A|B). Are the events A and B independent? Explain. Find P(B|A) and P(B|Ac). Are they equal? Show that P(Bc) ≠ P(Bc|A).
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