What are Exhaustive Events?
Exhaustive events, in the context of probability, refer to a set of events that collectively cover all possible outcomes of an experiment or situation. In other words, when we say that a set of events is exhaustive, it means that one of those events must occur. There are no other possible outcomes left.
For example, consider flipping a fair coin. The possible outcomes are heads (H) or tails (T). In this case, “getting heads” and “getting tails” are exhaustive events because they cover all possible outcomes when you flip the coin. The sample space, in this case, is {H, T}, and the events “getting heads” and “getting tails” are exhaustive since there are no other possible outcomes.
Mathematically, if E1, E2, ……., En are exhaustive events, their union (E1 ∪ E2 ∪ …… ∪En) equals the entire sample space (S).
Definition of Exhaustive Events
Exhaustive events in probability refer to a collection of events that together cover all possible outcomes of an experiment or situation.
In simpler terms, exhaustive events ensure that one of the events in the collection must occur, leaving no room for other outcomes. This concept is fundamental in probability theory as it ensures a comprehensive understanding and analysis of possible outcomes.
Exhaustive Events
Exhaustive Events are a set of events where at least one of the events must occur while performing an experiment. Exhaustive events are a set of events whose union makes up the complete sample space of the experiment.
In this article, we will understand the meaning of exhaustive events, its definition, Venn diagram of exhaustive events, collective exhaustive events, and examples of exhaustive events.
Table of Content
- What are Exhaustive Events?
- Exhaustive Event Venn Diagram
- Collectively Exhaustive Events
- Examples of Exhaustive Events
- Calculation of Probability for Exhaustive Events