Probabilistic Miracles: Why Nothing in Nature is Physically Impossible

The physically impossible differs from the logically impossible. It’s logically impossible that 2 plus 2 equals 5 or that a bachelor is married. On the other hand, it’s physically impossible to build a perpetual motion machine or for a human at a high-jump competition to clear 100 feet. The Second Law of Thermodyanmics is supposed […]

Lesson of the Monty Hall Problem

On the television game show Let’s Make a Deal, Monty Hall, the show’s best known host, used to present contestants with the following situation: the contestant would be presented with three doors behind one of which was a big prize (say a brand new car). Behind the other two doors was a small prize (say […]

The Bare Bones of Bayes’ Theorem

Thomas Bayes died over 200 years ago, but his legacy is still with us and provides some very useful insights into probability. What is his legacy? It is a probability formula that tells us how to update probabilities in light of new information. Suppose, for instance, you learn that Fred is a physical fitness fanatic […]

The Bare Bones of Probability

How likely is it that an event will happen? Probabilities attempt to answer this question by assigning numbers to the likelihood of events. A probability is always a number between 0 and 1. The closer to 0 the probability, the less likely the event; the closer to 1, the more likely the event. An event […]