Probability

Probability is a number that measures the degree of certainty attached to an outcome before it happens. It is expressed on a continuous scale running from 0 to 1: the value 0 denotes an impossible event, the value 1 a certain event, and any value in between an event that is more or less expected. The same information can also be expressed as a percentage, from 0% to 100%.

A useful mental image is that of a confidence slider. The closer the slider moves toward 1, the more the outcome is expected to occur; the closer it gets to 0, the more unlikely it is judged to be. At the center, at 0.5, both outcomes are equally plausible, as with a fair coin that lands on heads as often as on tails.

In the simplest case, where all outcomes are equally likely, the probability of an event is calculated by dividing the number of favorable cases by the total number of possible cases. With a fair six-sided die, rolling an even number corresponds to three favorable cases (2, 4, and 6) out of six possible cases, that is 3 divided by 6, which equals 0.5 or 50%.

Probability, which is a theoretical prediction, must be distinguished from frequency, which is a proportion actually observed after several trials. The former describes what should happen on average, the latter what actually happened. The two come together when the number of trials becomes very large.

A stubborn misconception is the belief that an outcome that is overdue becomes more likely. This is not the case when the draws are independent: the probability stays the same on every trial, with no memory of the past.

This notion is the common foundation of all the tools on the site. When a wheel of fortune, a die roll, a coin flip, a name draw, or a number generator produces a result, it is this measure that describes the chance of each possible outcome.