Notice that in the above exposition, the posterior probability is written as \(P(h_{\theta} \mid s_{n/5})\). Some expositions of Bayesian inference prefer to express the revised opinion as a new probability function \(P'( \cdot )\), which is then equated to the old \(P( \cdot \mid s)\).  For the basic formal workings of Bayesian inference, tis distinction is inessential. But we will return to it in  Section 4.3.3. 