Mutually exclusive and collectively exhaustive

We will be defining and discussing the terms mutually exclusive and collectively exhaustive during this week’s discussion. As human beings with free will, we encounter many situations that are not mutually exclusive and collectively exhaustive; however, we also face many problems that are mutually exclusive and collectively exhaustive despite this. Whether or not we realize it, we take these concepts into account when assessing the probability of events that we take part in. A mutually exclusive event is one that results in a single outcome, not simultaneously. The term collectively exhaustive defines events with lists of outcomes that include all possible outcomes (Render et al., 2014).

A few examples of mutually exclusive events include walking in a hallway with an option to go right or left, a test question with four answers, A, B, C, and D, or rolling a dice. With the previously mentioned examples, we can assess whether or not they are collectively exhaustive. In the case of walking in a hallway with the option to go right or left, provided that there are no doors or rooms to choose, this event would be defined as collectively exhaustive. When looking at the test question example proposed above, we can say that this situation is collectively exhaustive. Finally, we can also look at the dice example given above and say that this event would be collectively exhaustive. This is an interesting concept that I will keep in the back of my mind when making and assessing the decisions that I will make in the future.

References

Render, B., Ralph M. Stair, J., Hanna, M. E., & Hale, T. S. (2014). Quantitative analysis for management (2nd ed.). Prentice Hall.

Q2. A mutually exclusive event is an event in which only one result can come from the given trial.  Collectively exhaustive refers to the entire listing of possibilities to an event.  A collectively exhaustive list may have 50 possible outcomes, the mutually exclusive event is the single outcome that actually results from that list at the finale of an event.  For example, a rubik’s cube has 43 quintillion possible configurations.  Only one of the configurations has solid colored walls on each side.  In mixing a rubik’s cube, the 43 quintillion possibilities are the collectively exhaustive list of results.  Ending in a cube with solid colors on each side is the mutually exclusive event.  If the cube has the solid colors on every side, none of the other 42,999,999,999,999,999,999 events can occur at the same time.

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