Exhaustive Events
2026-02-28 08:26 Diff
https://brightchamps.com/en-us/math/data/exhaustive-events

In order to represent the exhaustive events more clearly, graphical representation using Venn diagrams can be of a great help to the students learning about probability, events, its types etc. Here is the Venn representation of the exhaustive events.

Let’s take an example, in a sample space of rolling a die S = {1, 2, 3, 4, 5, 6}. Event A of getting an even number on the die EA = {2, 4, 6}. Event B of getting an odd number on the die EB = {1, 3, 5}. Event C of getting a prime number on the die EC = {2, 3, 5}. 

Here, some numbers of the dice exist in both the events. So this event can be termed as an exhaustive event, but not mutually exclusive. Because mutual exclusive events should not overlap the numbers with other events of the same set.
    

1. First, find all the possible outcomes of a given event. 
 

2. Find the outcomes which overlap with other events (if possible, otherwise it will be a mutually exclusive event). 
 

3. Draw circles with the event that includes both outcomes of the other events placed at the center. Since Event C has both the outcomes of Event A and Event B, Event C will overlap both the other events and represent in the center. 
 

4. Event C = {2, 3, 5}; numbers 2 is in Event A, and 3, 5 overlap with Event B. Now write those outcomes in the overlapping part of the two circles.
 

5. Repeat the process for all the events.