Dennis Lindley's paper The Philosophy of Statistics in 2001 includes the following 'simple' example of statistical coherence: "A set of uncertainty statements is said to be coherent if they satisfy the rules of the probability calculus. Thus, the pair of statements p(A|B) = 0.7 and p(A| ~B) = 0.4 do not cohere with the pair p(B|A)= 0.5 and p(B|~ A) = 0.3. (Here ~B denotes the complement of B.) Think of A as a statement about data x and B as a statement about parameter theta. The first pair refers to uncertainties in the data and coheres with the first parameter statement, p(B|A)= 0.5, for data A. (Take p(B) = 0.4/1.1 = 0.36.) But all three do not cohere with the second parameter statement for data A, that p(B| A) = 0.3. With p(B) = 0.36, the coherent value is 0.22."
How is the coherent value of 0.22 calculated?