12. You must decide whether to eat at Burger Hut or Pizza King, two local restaurants that...

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12. You must decide whether to eat at Burger Hut or Pizza King, two local restaurants that are right next to each other. You have heard a few good things about Burger Hut, so your prior is that there is a 60% chance it is better; thus there is a 40% chance Pizza King is better. However, when you arrive to eat, you see one customer at Pizza King but nobody at Burger Hut. You believe that any person off the street, when given two options, will pick the better restaurant 75% of the time. Based on what you believe and what you have seen, what is the probability that Pizza King is the better restaurant?

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