1. ACME sells widgets both direct-to-consumer (DTC) via its online store and also to retailers. Suppose 25% of widgets sold by ACME are purchased through its online store, 66% of widgets sold are shipped from its distribution center (DC) in Chicago, and 16.5% fall into both categories. Calculate each probability. (a) A widget is sold DTC or shipped from the DC in Chicago but not both. Interpret this probability in context. (b) A widget is shipped from the DC in Chicago given it was sold DTC. (c) Are the events sold DTC and shipped from Chicago independent? Justify.

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