VENN diagrams extended to event complements for solving conditional probability and Bayes' theorem.

Abstract

All roads lead to Rome, goes an old saying. In the world of mathematics, a given problem has many ways of being solved, some of which can be complex and others very simple and straightforward. It is important to note that the person trying to understand or learn mathematics needs the quickest way of understanding.
Venn diagrams have been widely used in the solution of probabilities including the conditional and Bayes’ Theorem. However, we can use this technique to extend the complements of the events that are dealt with in each problem to optimize calculations and thus be able to answer all the probability questions that the problem relates to.
Within the technique is to form the interlocking circles indicating the common region for each of the events to be treated and thus their respective complements. As there are 2 events, 4 areas will be formed that have been named as petals, which are equivalent to the difference or sums with the total probability of each event as the case may be.