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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 [...]
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 [...]
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 [...]
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 [...]
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 [...]
Rediscovering Richard III of England: In September 2012, archaeologists unearthed remains from a Leicester car park, covering what was once the city’s medieval Franciscan friary. After five months of waiting and exhaustive scientific tests, those bones were revealed to be those of Richard III, the infamous last Plantagenet king of England and the last English King to die in battle.
Use Social Science to Improve Your Health: Social science research has uncovered many helpful tips on improving our health. Find proven methods to lose weight, become fit, quit smoking, manage drinking, improve mental health, reach goals and promote positive relationships with the help of modern social science and social media. Written by Gina Barrett Putt, M.A. in Sociology, this ebook features current research and take away points.
Flying is Fun! is based on the aviation articles which Helen Krasner wrote for the magazine Flight Training News during the years 2011 to 2012. It begins with an article from Helen’s early days of learning to fly, My Learning-to-Fly Nightmare, which should provide encouragement for anyone who is struggling with the PPL course. The next three articles are about topics of general interest to private pilots. Then come a group of helicopter related articles, but these should still provide food for…
Have you ever considered converting your WordPress Blog into a Multi-Author Website? It’s not as hard as you think. In fact, with this tutorial, you’ll be done in just one weekend! (Or much less, if you are comfortable with the WordPress interface.) This edition includes a simple checklist and easy-to-follow walkthroughs for all plugins. You’ll be managing multiple writers in no time flat!
The Hunter and the Scorpion: In an endless cosmic chase the scorpion pursues the hunter, his intended victim, as they run across the sky. The Hunter and the Scorpion begins with the mythological lore behind two prominent easy to locate constellations: Orion, the Hunter, and Scorpius, the Scorpion. The Hunter and the Scorpion however encompasses much more than a constellation guidebook. Integrating ancient mythology, constellation lore, and modern astrophysics it tells the life story of stars an…
Unsung Heroes of Modern Physics Of course you’ve heard of Albert Einstein, creator of special and general relativity, and other famous scientists – but there are many other physics pioneers who have received very little mainstream recognition for their contributions to history. Join Ira Mark Egdall, as he explores the fascinating history of five Unsung Heroes of Modern Physics. Despite extraordinary achievements in relativity, quantum mechanics, astronomy, cosmology, or space exploratio…
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