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Consider the following scenario. Suppose that your favorite…

Consider the following scenario. Suppose that your favorite restaurant serves the best ramen dishes in town. Since you eat there so often, you’ve observed the following: the patrons are 40% male, the probability that the patron orders a tofu-based meal given that the patron is male is 30%, while the probability that the order is tofu-based given the patron is female is 50%.  One night, you walk into the restaurant and see a tofu-based dish on one of the tables that is partially eaten, but the customer has already left. What is the probability that the customer was female?