Event

An event is what one seeks to measure the chance of in a random experiment. Concretely, it is a condition that the result may or may not satisfy, to which a probability is assigned. Rolling an even number with a die is an event, just like drawing a heart from a deck of cards or the wheel stopping on a red sector.

The mental image is that of a grouping of results. Among all the conceivable outcomes, an event gathers those that make it happen. It can be elementary when it corresponds to a single outcome, such as rolling a 4; it is compound when it groups several together, such as rolling an even number, which brings together the outcomes 2, 4, and 6.

An event is therefore always a subset of the sample space, that is of the set of all possible results of the experiment. For a six-sided die, the sample space consists of the outcomes 1 through 6, and the event even number is the subset made up of 2, 4, and 6.

When the outcomes are equally likely, the probability of an event is calculated by dividing the number of outcomes that make it up by the total number of outcomes in the sample space. The event rolling at least 5 groups two outcomes, 5 and 6, out of six possible, that is a probability of 2 in 6, in other words about 0.33.

The event should not be confused with its probability. The event is the description of the targeted result; the probability is the number that measures its chance. Two special cases deserve attention: the certain event, which gathers the entire sample space and has a probability of 1, and the impossible event, which contains no outcome and has a probability of 0.

On the site, each tool produces outcomes, and any question one asks about them defines an event. Asking whether a name draw will select a person from a given group, or whether a die roll will exceed a value, amounts to reasoning about events and their probabilities.