There are two possible states: {A, B}. Voters cannot observe the realized state. There is an incumbent politician who knows the true state. The politician can be of two types: g or b.

1.1 Suppose that everybody knows that a type g politician says A if and only if = A and a type b politician always says B. Using Bayes' rule, state what voters believe about the politician and the state if the politician says A.

1.2 Suppose that everybody knows that a type g politician says A if and only if = A and a type b politician always says B. Using Bayes' rule, state what voters believe about the politician and the state if the politician says B.

1.3 Suppose that everybody knows that a type g politician says A if and only if = A and a type b politician always says A if and only if = B. Using Bayes' rule, state what voters believe about the politician and the state if the politician says A.