An event is described as a set of outcomes. For example, getting a tail in a coin toss is an event while all the even-numbered outcomes while rolling a die also constitutes an event. An event is a subset of the sample space.
Occurrence of an Event
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Consider an experiment of throwing a die. Let’s say that event E is defined as getting an even number. So, if a number 4 comes up, it is said that event E has occurred.
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So, an event E of a sample space S is said to have occurred if the outcome w of the experiment is such that w ∈ E. When an outcome is such that it does not belong to the set E. It is said to have not occurred.
Composite Events:
Composite events in probability refers to the collection of some elementary events that have more than one probable outcome instead of a single estimated outcome. Composite events are applicable for mathematics and statistics to understand the probability of a group of events.
There are two types of composite events; one is ME and another one is MI. In this context, ME can occur in the presence of others whereas MI cannot occur in the presence of others.
For example, X and Y are two events.
- Formula for ME in probability: “P (X or Y) = P (X) + P (Y)” [P = Probability]
- Formula for MI in probability: “P (X or Y) = P (X) + P (Y) – P (X and Y)”