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Case Study: Imagine there are two types of majors: selfish and selfless. 60 percent of majors are selfish. Voters do not observe the type of the major. They instead observe whether the major decided to spend money on improving the facilities of the local school or the local casino. The voters know that most of the time the best use of money is to spend it on improving the facilities of the local school. 15 percent of the time there is a boom in tourism and in this special situation, the best course of action is to improve the local casino. Voters do not know if there is a boom in tourism. They only know that a good major will always do the correct thing (improve the local school in normal times and improve the local casino when there is a boom). They also know that selfish majors always improve the casino.
Question: What is the probability that the major is selfish after observing that the major built a casino?
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