I need two responses of at least 150 words each for the below students discussions for this week. Also in the bold below are the questions the students at answering.
What is the meaning of mutually exclusive events? What is meant by collectively exhaustive? In your responses, please give an example of each. Please also comment on the examples provided by other students in your responses to others.
Growing up we have all heard the statement, “You can’t have your cake and eat it too.” This colloquial idiom is a great example of a statistically mutually exclusive event. A mutually exclusive event are things that cannot happen at the same time. In the case of the cake example, it is impossible to have your cake in front of you and eat it at the same time. A physical example of this would be running forwards and running backwards. These cannot occur simultaneously. Another example would be that of flipping a coin, it is impossible for it to be heads and tails at the same time. It can only be one or the other. This makes it mutually exclusive (George, 2018).
Collectively exhaustive means that the set of events covers all of the probabilities or that the chance of one of them occurring is 100%. An example of this would be when you roll a six-sided die because any roll will be representative of the set. To better understand this definition, it is important to define probability space, which consists of three parts: sample space, Event space, and probability function. A sample space is the set of all the possible outcomes. Event space is the set of all the events. Probability function is the assignment of the probability to the event. An example of this is rolling of a dice. Since any of the six events must be represented by one set (George, 2018).
I found it interesting that the examples of the die and the coin illustrate examples of both collectively exhaustive and mutually exclusive. For the die example, it is not possible to roll a 2 and a 1 on the same roll, making it mutually exclusive as well. For the coin example, there is no other possibility besides heads or tails, making it collectively exhaustive.
George, K. (2018, August 16). Mutually Exclusive & Coll. Exhaustive. Retrieved from Survey Tips. Researching & Marketing Strategies: https://rmsresults.com/2010/04/27/mutually-exclusi…
What is the meaning of mutually exclusive events?
Mutually exclusive events are simply event that cannot take place at the same time (Young, 2019). Mutually exclusive events are also independent events, meaning that they do not have to occur simultaneously. In mutually exclusive events, the occurrence of one event prevents the possibility of another event/events occurring (Mutually Exclusive Events, 2009). A great example of this is when a quarter is flipped. There are two possibilities that could occur. You can either get heads or tails when the coin lands, but you cannot get both. Also, getting tails the first time does not necessary mean you will get heads if you flip the coin again. This also means that getting heads when the coin is flipped prevents you from getting tails simultaneously. Keep in mind that mutually exclusive events cannot coincide and the occurrence of one outcome supersedes the other outcome (Young, 2019). These events are independent events and have no impact on the viability of other options. So all both sides of the coin are considered independent events because they cannot occur simultaneously.
What is meant by collectively exhaustive?
Collectively exhaustive describes events in a probability theory where one of the events is bound to occur. What I mean by that is if you role a die with 6 sides, you know that one of the numbers from 1, 2, 3, 4, 5, and 6 is bound to occur. This event is considered collectively exhaustive because one of the outcomes is bound take place. In this scenario, the entire range of possible outcomes is included and one of those events in the range will definitely occur when the die is rolled. Is it known as “Collectively exhaustive” because all the events put together make up every possibility that can take place.
Mutually Exclusive (Events). (2009). Retrieved from http://search.credoreference.com/content/entry/pen…
Young, J. (2019, August 17). Mutually Exclusive Definition. Retrieved from Investopedia: https://www.investopedia.com/terms/m/mutuallyexclu…