This paper presents an alternative version of formulas of conditional probabilities and Bayes' rule that demonstrate how the truth table of elementary mathematical logic applies to the derivations of the conditional probabilities of various complex, compound statements. This new approach is used to calculate the prior and posterior probabilities of conditional statements by means of probability logic table along with the Bayesian principle. Unlike the more commonly used methods, such as the formula, tree diagram, and contingency table, a probability logic table approach represents a convenient, straight-forward, and useful method for calculating and teaching conditional probability and Bayes' rule to statistical novices whose reasoning processes are fundamentally different from that of the expert. The use of a truth, or probability logic table is illustrated in comparison to the formula, tree diagram, and contingency table methods. The problem to be resolved is one frequently used in finite mathematics and elementary statistics courses, that of determining the probability of observing a family with three children. It is argued that a truth table approach is less complex and time consuming than the traditional methodologies.