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."
(a) Find P(A), P(B), and P(A | B).
(b) Are the events A and B independent?
(c) Find P(B | A) and P(B | Ac). Are they equal?
(d) Show that P(Bc) ?= P(Bc | Ac).
Part D asks to show that the Probability of B complement does not equal the Probability of B complement given A complement.