 The Principal Principle is important perhaps mainly because of its extensive applications in Bayesian statistics, in which this principle is more often called the Direct Inference Principle. To illustrate, suppose that you are somehow certain that one of the following two hypotheses is true: \(H_1 =\) “the coin has a bias 0.4” and \(H_2 =\) “the coin has a bias 0.6”, which are paradigmatic examples of “ordinary” hypotheses. Then your credence in the first hypothesis \(H_1\) given evidence \(E\) that the coin lands heads ought to be expressible as  follows:[6]