Mutually Exclusive & Exhaustive System of Events

The notion of mutually exclusive events deals with the occurrence of the events when the events are disjoint towards each other. The definition further states that the occurrence of two events is said to be mutually exclusive when both events cannot happen at the same level of time. The notion of exhaustive events deals with the occurrence of the events when the events include the same sets of sample space. The chances of all the probable events within a sample space could be defined as exhaustive events. The concepts of a mutually exclusive event and exhaustive events both are parts of the probability distribution.

What are mutually exclusive and exhaustive systems of events?

The idea of mutually exclusive events states that the occurrence of two events must be collective. The happening of two events is said to be mutually exclusive when two events cannot occur at the same time. The occurrence of the two events could not happen at the same time when the mutually exclusive event occurs. The other name of the mutually exclusive event is disjoint events. In the sets of mutually exclusive events, the occurrence of one event does not depend on the occurrence of the other event. 

The idea of an exhaustive system of events could be divided into two categories namely exhaustive event and mutually exhaustive event. The concept of exhaustive events states that the occurrence of one event within a sample space is necessary while carrying out an experiment. The concept of the mutually exhaustive event states that when the experiment is taking place the occurrence of both events are not possible at the same point of time. 

Example of mutually exclusive events

The notion of mutually exclusive events is used in the probability distribution to identify the type of event. An example of a mutually exclusive event is the tossing of a coin. When the experiment of tossing a coin happens then the head and tail could not occur at the same time. In the experiment of tossing a coin, either a head or a tail will occur as a resulting output. This example clearly explains the aspects of the mutually exclusive events when an experiment takes place. The concept of the mutually exclusive event is also used in figuring out some calculations in the financial aspects. The implementation of mutually exclusive events is useful in the process of calculating capital budgeting and the net present value of the financial segments. The implementation of mutually exclusive events is used to evaluate the aspect of various financial events. This financial event promotes better analysis of the future operational forecasting system. 

Example of an exhaustive system of events

The example of an exhaustive system of events could be used in various ways.  An example of an exhaustive system of events is rolling a die. When a die is rolled the number of possible outcomes is six, which are {1, 2, 3, 4, 5, 6}. The total number of possible outcomes could be exhaustive as the number 2 and number 6 can occur at the same time. When two such outcomes have the possibility of occurring at the same time then it could be termed as an exhaustive system of events. The concept of the exhaustive event states that at least one of the outcomes necessarily happens at the time of experimenting with an event. The union of two events when becomes equal with the sample space then the two events are said to be an exhaustive system of events. The happening of the experiment is said to be an exhaustive system of events when at least one of the outcomes occurs at the time of performing an event. 

Difference between a mutually exclusive and exhaustive system of events

The major difference between a mutually exclusive event and an exhaustive system of events is that the mutually exclusive event occurs when the two outcomes cannot occur at the same time whereas the exhaustive system of events occurs when the two outcomes can occur at the same time. Sometimes the nature of exhaustive events could or could not be mutually exclusive. On the other hand, no mutually exclusive events are an exhaustive system of events. The outcome and the happening of the events depend on the nature of the events in an experiment. The mutually exclusive and exhaustive system of events is different in the aspect of implementation.

Conclusion

This could be concluded by stating that identification of the nature of the events is necessary to resolve the problems regarding probability distribution. The discrimination between the natures of events helps to categorize them in different ways and helps to understand their nature as well. The implementation of a mutually exclusive and exhaustive system of events could be used in the pathway of predicting any issue. The tossing of a coin and the throwing of dice could be analyzed with the help of these two types of events. The different aspects of the events have been evaluated in this assignment with proper examples and their usage. The different types of events are the different segments of the probability distribution.