In a decision problem where we wish to use Bayes' theorem to calculate posterior probabilities, we should always begin our analysis with the assumption that all states of nature are equally likely, and use the sample information to revise these probabilities to more realistic values.

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In a decision problem, it is not always appropriate to assume that all states of nature are equally likely. The prior probabilities should be based on any available information, such as historical data or expert opinions, and then updated using Bayes' theorem as new information is obtained from the sample.

In a Decision Problem Where We Wish to Use Bayes