Probability

The probability of an event is typically expressed as the percentage of ways it might happen, out of a number of possible events. The chance of a tossed coin coming up heads is 50%, because there is 1 way it can happen, out of 2 possible ways. 1 / 2 = 0.5 or 50 percent.

Probability is represented as a number between 0 (representing impossibility), and 1 (representing certainty). Sometimes percentages are used, with numbers from 0% to 100%.

The letter P is used to indicate the probability of some event. For example P(heads) could represent the probability of tossing heads on a coin. More generally, probability can be described in terms of events. These relate to set theory in the following way. The sample space S can be thought of as the set of all possible outcomes. P(S) = 1, as it is certain that one outcome must occur. An event can be thought of as a subset of S. For example, heads would be the subset of the outcomes where heads is tossed on a coin.