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In an elementary study of synchronized traffic lights, consider a simple four-light system. Suppose that each light is red for 30 seconds of a 50-second cycle and suppose P(S;+IlS;) = 0.15 and P(S;+1|S;) = 0.40 for j = 1, 2, 3, where S, is the event that a driver is stopped by the jth light. We assume a "one-light" memory for the system. Determine the probability that a driver a) Will be delayed by all four lights. b) Will NOT be delayed by any of the four lights. c) Will be delayed by at most one light