Probability

A probability, colloquially called a chance, is a mathematical value or function that represents a variety of concepts, most commonly the likelihood of a given event occurring, but has been interpreted in many different ways, such as a measure of confidence. Formally, a probability is

• defined in $[0,1]$ and therefore both limited and non-negative;
• normalized: a set of probabilities $\{ P_{i} \}$ describing all $n$ possible outcomes of an event must add up to 1: $\sum_{i=1}^{n}P_{i}=1$.

One way of defining probability is to see it as a ratio of number of desired outcomes over total possible outcomes:

Say for instance we roll a six-sided dice. If the die is fair and not weighted, all the sides have equal chances of coming up on a roll, so if we want to roll exactly 4, that is one desired outcome over six possibilities. The probability of this occurring is therefore