The term mutually exclusive means that two events have no common elements in them. The occurrence of one event means that the other other event does not occur. An example of a mutually exclusive event could be rolling a die, possibility A would be the number rolled is even and possibility B would be the number rolled is odd. The two possibilities (A and B) are mutually exclusive because all outcomes from rolling the die cannot be both possibility A and B at the same time.

In a discrete probability distribution there are different values of x, each value is unique and mutually exclusive events. Any event that occurs shall have only one possible value of x under, this ensures that the sum of all probabilities of x will equal 1.

An example could be with a deck of cards, let's say x has values A, B, and C. The values represent the events of a red card, face card, and black card. There will be instances where a card drawn falls under 2 values. Such as a King of Hearts, this would be event A and B, therefore it would be counted twice. The events that are counted twice would make the sum of all probabilities greater than 1, which is not possible. The sum needs to be less than or equal to 1.

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