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Two events are not mutually exclusive if both events can occur at the same time. These events have common elements. They are also called inclusive events.

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Two events are mutually exclusive if both events CANNOT OCCUR AT THE SAME TIME. These events HAVE NO COMMON ELEMENTS. They are also called DISJOINT EVENTS.

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Venn Diagram of Mutually Exclusive Events.

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If two events, A and B, are mutually exclusive, then the probability that either A or B occurs is the sum of their probabilities.

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A card is drawn from a deck of standard playing cards.

Event A: An ace is drawn.
Event B: A king is drawn.

Events A and B are mutually exclusive since you can only get an ace or a king but not both and there is no element in common.

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Observe that the events intersect each other. This only shows that there are elements in A and in B that occur at the same time. The intersection of A and B should be subtracted to eliminate elements being duplicated.

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If A and B are two not mutually exclusive events, then the probability of A or B occurring is both of their probabilities added together and subtracting the probability of both of them occurring.

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A card is drawn from a deck of standard playing cards.

Event A: A heart is drawn.
Event B: A king is drawn.

Events A and B are not mutually exclusive or NON- mutually exclusive since the king of hearts is common to both hearts and kings.