An Explanation on How to Define Mutually Exclusive Events

The mutually exclusive events are considered a pair of non-overlapping events and these are very different from the independent events. The independent events can happen anytime and can overlap each other. It means that the events in independent events are spontaneous whereas the events in mutually exclusive events are not spontaneous. The mutually exclusive events offer very important applications in finance and the other branches of mathematics. These events are also known as the disjoining events for their characteristics and in mathematical language, which can be described as the events whose probability to happen at the same time is equal to zero.

The Calculation Process of Mutually Exclusive Events

Mutually Exclusive events, also known as disjoining events, are events that cannot take place at the same time. The best example of these types of events is the tossing of a coin. The head and tail parts cannot be the result at the same time. The result will be either the tail or the head and so these events can be considered mutually exclusive events. The probability of events in every mutually exclusive event is zero. There are two types of symbols to symbolize the relationships between two types of sets. The first one is supposed to show intersection sets and the other one is to show the union sets. These signs seem just opposite to each other. 

Probability and Representation of Mutually Exclusive Events and Types of Sets

The probability of events in disjoint events, A and B, is always equal to zero. The specific rules for addition apply to a pair of mutually exclusive events. The probability for the union set of event A and event B will be equal to the sum of the probabilities of event A and B. Venn diagram is used to represent a pair of mutually exclusive events, where two circles are used to represent two events and the circles will take place separately in the diagram. It means that the circles will not even touch each other. The highest probability of events in mutually exclusive events can be equal to one in some special cases. Therefore, the probabilities of two events, A and B, are considered zero and the conditional probability formulas of the probability of events are as follows:

P(A or B)=P(A)+P(B)

Rules of Mutually Exclusive events

According to the theory of probability of events, a pair of events will be mutually exclusive events if they are not overlapping each other. An event like tossing a coin is an example to describe the rules of events. The probability for both of getting head or tail is 50%, where these events cannot overlap each other in the period. Therefore, the sum of the probability for events is equal to zero. The probability will be equal to one of the same pair of events are also an exhaustive event. Otherwise, the probability of events will always be less than one. One of the applicable rules for the mutually exclusive event is that the union of events will always be equal to the sum of the probability of events. The rules for the mutually exclusive events show that the mutually exclusive events have different properties from the independent events. 

Conclusion

Some of the mutually exclusive events are included in daily life and one of them is the left and right rotation of an arm. This is a mutually exclusive event because the left rotation of an arm cannot be done during the right rotation of the same arm. According to the conditional probability formulas, the union of a mutually exclusive event is equal to the sum of the probability of events. The union of an independent event is equal to the subtraction from the sum of the probability of events to the multiplication of both events. The mutually exclusive events teach students about the probability theory of events and the conditional probability formulas.