Assess hypotheses by calculating their probabilities \( p(H_i | \ldots) \) conditional on known and/or presumed information using the rules of probability theory.

Probability Theory Axioms:

Product (AND) rule :

\( p(A, B | I) = p(A|I) p(B|A, I) = p(B|I)p(A|B,I) \)
Should read \( p(A,B|I) \) as the probability for propositions \( A \) AND \( B \) being true given that \( I \) is true.

Sum (OR) rule:

\( p(A + B | I) = p(A | I) + p(B | I) - p(A, B | I) \)
\( p(A+B|I) \) is the probability that proposition \( A \) OR \( B \) is true given that \( I \) is true.

Normalization:

\( p(A|I) + p(\bar{A}|I) = 1 \)
\( \bar{A} \) denotes the proposition that \( A \) is false.