Modified version of Let's Make a Deal: Suppose you believe that there is a 0.1 probability that the car is behind door 1, a 0.3 probability that it is behind door 2, and a 0.6 probability that it is...

Modified version of Let's Make a Deal: Suppose you believe that there is a 0.1 probability that the car is behind door 1, a 0.3 probability that it is behind door 2, and a 0.6 probability that it is behind door 3. Which door should you choose initially? Should you switch when the host shows you a goat?

For each of the following, provide an example:

A. A distinction that does not pass the clarity test.

B. A distinction that is clear, but not observable.

C. A distinction that is clear, observable, but not useful for the decision.