## Conditional Probability is Not Commutative: Formulas and Examples

Confusing the “given” event (the event that you assume to have occurred) with the combined event (for which you are calculating probability) is a common pitfall with conditional probability. A Recap of Conditional Probability Recall that “the conditional probability of event ‘A’, given that event ‘B’ has occurred, is calculated as the probability that both [...]

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## An Introduction to Calculating Conditional Probability in Mathematics

Despite the value of knowing the probability of an event before it occurs, it can be even more valuable to know how learning part of the outcome changes the conditional probability. The Foundation for Understanding Conditional Probability This article continues a series about probability, by introducing “conditional probability.” If the terms are unfamiliar, consider reviewing [...]

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## Axioms and Two Useful Theorems of Discrete Probability Functions

The first article in this series, Introducing Probability Theory without Statistics, noted that probability distribution might be “discrete” or “continuous.” This article builds the foundation for discrete probability functions, by introducing the four axioms and deriving two useful theorems from them. Discrete Probability Functions: The Soul of Discretion The phrase, “probability distribution”, refers to the [...]

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## The Probability of the Allais Paradox in Lottery Preferences

One marvelous example of the conflict between mathematics and human behaviour is shown in the “Allais Paradox.” Compared to probability theory, in the Allais Paradox, people choose correctly or incorrectly based on irrelevant details. Probability, Payout, Expected Value and Lotteries The mathematical view of “probability” is the likelihood that some specific outcome will occur from [...]

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## Introducing Probability Theory without Statistics

This article introduces basic mathematical concepts in probability. Future articles will discuss different aspects, including several paradoxical situations involving probabilities. For those who can’t wait, Solve the Monty Hall Problem using Logic and Mathematics. Probability, Statistics or Likelihood? In mathematics, “probability” is the study of how likely it is for some specific outcome to occur [...]

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