Mutually Exclusive events are two events which will never occur at the same time (Perekupka, 2003). In simple terms, in mutually exclusive events, if one event will happen, the other event will surely not happen in that time. In statistical terms, the probability of mutually exclusive events to happen at the same time is zero (Perekupka, 2003). That would also mean that adding the probability of the two events would result to 1. An example of mutually exclusive events would be the concept of passing or failing a certain course. In the rules imposed in all educational systems, there is no exception about rules of passing and failing. No student can pass and fail at the same time, but one thing for sure is that either passing or failing will bound to happen in the future depending on the variables which might affect the results.
Not to be confused with mutually exclusive events, collectively exhaustive events are group events in which at least one of the events will happen (Transtutors, 2007). The difference of collectively exhaustive events from mutually exclusively events is that in the former, there are other possibilities of occurrence between the events. For example, when rolling a die, there are six possible outcomes, and one of the faces will occur when the rolling is triggered. The probability of the outcomes might be the same or not, but like in mutually exclusive events, the sum of all probabilities is also equal to one (Transtutors, 2007). This also implies that in collectively exhaustive events, the possibilities of the occurrence of events cannot be altered, but can be influenced, depending on the circumstance. Back to the example of tossing the die, the outcome will surely be one of the faces, and the outcome might be influenced on how the die was tossed.
References
Collectively Exhaustive Sets. (2007). Retrieved January 16, 2016, from http://www.transtutors.com/homework-help/statistics/probability/rules/collectively- exhaustive-sets.
Perekupka, M. (2003). Mutually Exclusive in Statistics: Definition, Formula & Examples. Retrieved January 16, 2016, from http://study.com/academy/lesson/mutually-exclusive- in-statistics-definition-formula-examples.html.
