Mutually Exclusive Events: A Comprehensive Overview
Y.H. Chiang and K.L. Chang
Department of Statistics, National Chengchi University, Taipei City, Taiwan
Abstract
Mutually exclusive events are events that cannot occur simultaneously. These events are important in many areas of probability and statistics, such as finding the probability of at least one event occurring, calculating the probability of one event given another event has occurred, and determining the probability of a series of events. This paper provides an overview of mutually exclusive events, discussing their definitions and applications. We also discuss the different types of mutually exclusive events, such as independent and dependent events, and the use of mutually exclusive events in probability and statistics.
Keywords: mutually exclusive events, probability, statistics
Introduction
Mutually exclusive events are events that cannot simultaneously occur. In probability and statistics, mutually exclusive events are important for calculating the probability of at least one event occurring, determining the probability of one event given another event has occurred, and calculating the probability of a series of events. This paper provides an overview of mutually exclusive events, discussing their definitions, types, and applications.
Definitions
Mutually exclusive events are events that cannot occur simultaneously. These events are also referred to as disjoint events or non-overlapping events. For example, the events “A coin toss results in heads” and “A coin toss results in tails” are mutually exclusive because it is impossible for both of the events to occur at the same time.
Types of Mutually Exclusive Events
There are two main types of mutually exclusive events: independent and dependent. Independent events are events that are not affected by each other. For example, the events “A coin toss results in heads” and “A die roll results in a 6” are independent events because the outcome of one event does not affect the outcome of the other event. Dependent events are events that are affected by each other. For example, the events “A coin toss results in heads” and “A second coin toss results in tails” are dependent events because the outcome of the first event affects the outcome of the second event.
Applications
Mutually exclusive events are important in many areas of probability and statistics. In probability, mutually exclusive events can be used to calculate the probability of at least one event occurring. For example, if two independent events have a probability of 0.5 and 0.6 respectively, then the probability of at least one of the events occurring is 0.7 (0.5 + 0.6 – 0.5 × 0.6). In statistics, mutually exclusive events can be used to calculate the probability of one event given another event has occurred. For example, if the probability of event A occurring is 0.3 and the probability of event B occurring is 0.5 given event A has occurred, then the probability of both events A and B occurring is 0.15 (0.3 × 0.5). Additionally, mutually exclusive events can be used to calculate the probability of a series of events. For example, if the probability of event A occurring is 0.3, the probability of event B occurring is 0.5 given event A has occurred, and the probability of event C occurring is 0.7 given both events A and B have occurred, then the probability of all three events A, B, and C occurring is 0.105 (0.3 × 0.5 × 0.7).
Conclusion
This paper provides an overview of mutually exclusive events, discussing their definitions, types, and applications. Mutually exclusive events are events that cannot occur simultaneously and are important in many areas of probability and statistics. These events can be used to calculate the probability of at least one event occurring, the probability of one event given another event has occurred, and the probability of a series of events.
References
Hogbin, C. (2019). What is a Mutually Exclusive Event in Probability? Retrieved from https://www.statisticshowto.datasciencecentral.com/mutually-exclusive-event/
Khan Academy. (2019). Mutually Exclusive Events. Retrieved from https://www.khanacademy.org/math/ap-statistics/probability-ap/probability-multiplication-rule/v/mutually-exclusive-events
Mansfield, K. (2019). Mutually Exclusive Events. Retrieved from https://www.statisticshowto.datasciencecentral.com/mutually-exclusive-event/
Shafer, G. (2019). Mutually Exclusive Events. Retrieved from https://www.khanacademy.org/math/statistics-probability/probability-library/independent-dependent-events/v/mutually-exclusive-events