39. A large food processor operates three processing plants on the west coast. The plants, labeled 1, 2, and 3, differ in size, and produce 20, 35, and 45 percent of the food processor’s total output of spinach, respectively.

Given past history of USDA inspections for sanitation, the probability of a contaminated box of spinach emanating from each of the three plants can be assumed to be .0001, .0002, and .0005, respectively.

Contamination of the food processor’s spinach product with Ecoli was identified in a box of spinach shipped to an east coast grocery store, but the bill of lading has been misplaced on the shipment so that it is not known from which plant the shipment originated from. Let Ai,i ¼ 1, 2, 3, denote the events that a box of spinach came from plants 1, 2, and 3, respectively. Let the event C denote