What is Bayes’ Theorem? Bayes’ Theorem can be interpreted in several ways, but it requires us to introduce more definitions and terminologies, depending on the applications. Since our goal is to keep things simple and intuitive, we say that Bayes’ Theorem is a formula for inverting conditional probability: $$P[A|B] = \frac{P[B|A]\cdot P[A]}{P[B]}$$ Think about the following…
What is the Inclusion-Exclusion Principle? The Inclusion-Exclusion Principle may sound fancy but it is nothing more than a counting strategy. The Principle of Inclusion-Exclusion provides a method to find the size of the union of a group of sets, given the size of each set and the size of all possible intersections among the sets. To illustrate, we take a look at…
The Inclusion-Exclusion Principle is a counting technique in Probability and Combinatorics. The idea is simple, yet it always feels more difficult when solving problems. However, It does not have to be difficult. We use sample questions for Exam P from the Society of Acturaries to illustrate how we can break things down and how it…