Mutually Exclusive and Exhaustive System of Events

In this study, focus is given to conducting an exploration that has been a chapter of probability providing a major focus on conditions. This condition deals with “mutually exclusive” and as well as the “exhaustive system of events”. Moreover, the study successively explored defining the notions of mutually exclusive and events of exhaustive systems. As we all know, probability determines a measure of the likelihood of the events that occur within the experiments that are random in nature. The notion of probability is a quantified aspect that has a value between 0 to 1. It can also be stated that the “0” indicates impossibility and on the other hand, “1” indicates certainty.

Understanding Mutually Exclusive & Exhaustive System of Events

The notions of “Mutually Exclusive” and “Exhaustive Systems” are quite common in their usage in the field of probability. These terms are the conditions that determine what will be the result of the given random experiment. In the notion of mutually exclusive, two events are considered, that will be known as mutually exclusive if the two events cannot happen at the same time or rather simultaneously. They also refer to disjoint events and the probability among them will have the value “zero”. On the other hand, the notion of an “Exhaustive System” determines that an event needs to occur.

What is an exhaustive event in probability?

In the field of probability, logic and theory are the dominant aspects and basically refers to a particular set of events that are said jointly or rather collectively exhaustive, when at least there lies an occurrence of the events. It can be stated by an example, such as, if a six-faced dice are rolled, the events will have outcomes, consecutively 1, 2, 3, 4, 5, 6 respectively for a single dice and thereby termed as “collectively exhaustive”. This is also because the outcomes are a range of possibilities.

What are mutually exhaustive events in probability?

“Mutually exhaustive” is used when one event can happen only for a single time and not any more time.  In addition to these, it can also be stated that the occurrences will happen for one time on a definite basis on performing the experiments. These can also be termed as “mutually exclusive collectively exhaustive events”.

Meaning of exhaustive events in probability

The definite meaning of exhaustive refers to the condition that when experiments are performed one of the selected outcomes will occur at least one time. The set of exhaustive events is known as “collectively exhaustive” if they cover spaces of all probabilities. This means that the probability of anything happening to any of the outcomes will be 100 percent, therefore referring to be true for at least one.

What are mutually inclusive events?

The term mutually inclusive is very commonly used in the chapters of probability and it determines the overlapping of events with one another. A very common example is that of “buying off” an alarm system, another example may be buying seats for buckets. This is because both events can occur simultaneously and at the same time. On the other hand, mutually external events refer to the condition when no two events can happen or can occur at the same time.

Events and types of events

Several events are noticed with respect to the chapters of probability in mathematics that are as follows.

• Impossible and sure events
• Simple events
• Events that are compound
• “Independent and Dependent Events”

Conclusion

In this study, an exploration of the notion of probability is conducted that determines the condition for that the occurrences of random events are catered to. Furthermore, within the study, the focus has been provided based on certain events, one of which is exhaustive and also mutually exhaustive respectively. The meaning of these events is noted and is successively explained with their respective examples. Four main types of probability are noted to be “empirical”, “axiomatic”, “classical” and as well as “subjective”. Furthermore, a vivid understanding is made that caters to the aspects of possibility. The formula that is derived in figuring out the probability quotient is the total number of outcomes that are favoured divided by the total number of outcomes with the experiment.