A random variable (also called stochastic variable) is a variable that can take a set of possible different values, each with its own probability. For example, the experiment could be picking a person at random, and a random variable would be the person’s height. A random variable can be discrete or continuous. Discrete random variables […]

I saw this problem in a Probability course offered by the Harvard Extension program. I highly recommend it if you have the time. Here’s the problem: In Solomon’s reign there were two types of prophets: true prophets, who spoke the truth 9 out of 10 times, and false prophets, who only spoke the truth 5 […]

Before I explain what the prosecutor’s fallacy is, here’s a real life example where it affected (for the worse) the life of someone. Sally Clark was a British solicitor, and in 1996 his first son died, only weeks after his birth. In 1998 the same pattern occurred, when his second son died only weeks after […]

Thomas Bayes was an English minister and mathematician, and he became famous after his death when a colleague published his solution to the “inverse probability” problem. Described below. Given that you have a urn with 10 black balls and 20 white ones, what’s the probability that by picking randomly you’ll get a white ball? This […]

First things first: what is probability? Probability is a measure or estimate of how likely a certain event is to happen. Another way to put it: how likely a statement is to be true. Probability theory is the branch of mathematics concerned with these measurements and estimations. It’s a relatively new branch (when compared to […]

The classic birthday problem goes like this: there are N students in a classroom. What’s the probability that at least 2 of them will share the same birthday? Consider that a year has 365 days, and that a person has an equal chance of being born on each day. Let’s say N = 23 (you’ll […]