Let's examine the main differences between overlapping and mutually exclusive events.
Mutually Exclusive
Overlapping Events
Do not have outcomes in common
Can have outcomes in common
The probability is given by the sum of the probabilities of each individual event.
Since common outcomes are counted twice, the probability is the sum of the probabilities of individual events minus the probability of the events occurring together.
Mutually Exclusive Events
Let's describe an example of mutually exclusive events. Consider the numbers from 1 to 10.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Suppose that we randomly choose a number from the set and want to analyze the event of getting a number that is oddandeven. Since a number cannot be even and odd at the same time, these events are mutually exclusive.
Overlapping Events
Again, let's consider the number from 1 to 10.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Suppose that we want to analyze that a randomly selected number of the set is even or prime. Note that the number 2 is even and prime. Therefore, we have overlapping events. Please note that there are many possible examples of overlapping and mutually exclusive events.
