Combinatorics is a branch of mathematics with applications in fields like physics, economics, computer programming, and many others. In particular, probability theory is one of the fields that makes heavy use of combinatorics in a wide variety of … [Continue reading]

## Calculating Compound Event Probabilities

Probabilities can be thought of as measures of uncertainty in the occurrence of an event, the truth of a hypothesis, and so on. These measures are numbers between 0 and 1. Zero means the event is impossible to occur and 1 means the event is certain … [Continue reading]

## Probability: What Is It, Really?

Throughout history, we have come up with better and more accurate ways to measure physical quantities like time, length, mass, and temperature. This has been crucial for our scientific and technological development. Each of these quantities has a … [Continue reading]

## Coin Bias Calculation Using Bayes’ Theorem

Why do people flip coins to resolve disputes? It usually happens when neither of two sides wants to compromise with the other about a particular decision. They choose the coin to be the unbiased agent that decides whose way things are going to … [Continue reading]

## An Intuitive Explanation of P-Values

If you ever took an introductory course in statistics or attempted to read a publication in a scientific journal, you know what p-values are. Оr at least you've seen them. Most of the time they appear in the "results" section of a paper, attached to … [Continue reading]

## The Inverse Problem and Bayes’ Theorem

What will happen if you grab a solid rock and throw it at your neighbor's window? The most common result is that the window will break. If your neighbor later asks if you know anything about the incident, you can confidently inform him that his … [Continue reading]

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