Joshua and his army are planning to circle Jericho seven times. Will the wall come tumbling down? The king of Jericho reports that:
- I ascribe probability 0.8 to "the wall of the city will fall, and Joshua ascribes probability 0.6 to the wall falling."
- I ascribe probability 0.2 to "the wall of the city will not fall, and Joshua ascribes probability 0.5 to the wall falling."
Answer the following questions:
(a) What is the set of states of nature corresponding to the above description.
(b) What is the king's first-order belief? What is his second-order belief?
(c) Can Joshua's first-order belief be ascertained from the above description? Justify your answer.