Event

In a random experiment, an event is a set of outcomes that has some probability of occurring. Each set of outcomes satisfies some condition. Given a fair 6-sided die, an example of an event is "rolling an even number." The set of outcomes that satisfies this condition is: {2, 4, 6}. The probability of rolling an even number is 3/6, or 50%, since the sample space of the experiment is all the potential outcomes of the roll of the die: {1, 2, 3, 4, 5, 6}.

Types of events

There are many different types of events that are considered in probability and statistics including independent events, dependent events, compound events, and more.

Independent events

Independent events are events in which the outcome of an event is unaffected by the outcome of another. Given a fair coin, there is an equal probability of heads or tails occurring on any given flip of the coin. The coin landing on heads does not affect the probability of heads or tails occurring on any subsequent flip.

Dependent events

A dependent event is an event in which the outcome of the event is affected by the outcome of some other event. If there are 3 blue marbles and 2 red marbles in a bag, and one marble is removed from the bag, there is a 60% chance that the marble is blue, and a 40% chance that the marble is red. If a blue marble is removed from the bag, then there are now 2 blue marbles and 2 red marbles, so the probability of either being removed becomes 50%.

Compound events

A simple event is one that has only one outcome. It makes up one point of the sample space. Given the sample space {1, 2, 3}, event E = {1} is a simple event.

In contrast, a compound event has more than one possible outcome. In other words, it is made up of more than 1 simple event. Given the sample space {1, 2, 3}, E = {1, 2} and E₂ = {1, 2, 3} are both compound events.

An example of a compound event is the outcome of rolling two dice. Each die can result in 1 of 6 outcomes. Rolling only one die is an example of a simple event.

Mutually exclusive events

Mutually exclusive events are events that do not share any common points. For example, in the set of all real numbers, the set of odd numbers ({1, 3, 5, 7, 9...}) and set of even numbers {(2, 4, 6, 8, 10...}) are mutually exclusive. Another example of mutually exclusive events are the outcomes of the flip of a coin. The coin cannot land on both heads and tails, only one or the other.