Mutually Exclusive Events: Two
events are mutually exclusive if they cannot occur at the same time. In tossing
of a coin, either of head or tail flips meaning they are mutually exclusive. An
occurrence of head excludes an occurrence of tail in the same toss.
Figure 1: Marginal probabilities in tossing of a coin
Likewise,
in drawing a card from the deck of 52 cards, the occurrence of an ace card
excludes cards of other ranks, two to ten, jack, queen and king. Let A be an event
of drawing an ace card. Likewise, let B
be an event of drawing any non-ace card. The marginal probability of A, P(A) is four by
52 or one by 13. Similarly, the marginal probability of any non-ace card, P(B)
is 48 by 52 or 12 by 13. The joint probability of ace and any non-ace card in a
single draw, denoted by P(A and B) is impossible, equal to zero.
Figure 2: Marginal probabilities in drawing a card from a deck
Mutually Inclusive Events: Two events are mutually inclusive or non-exclusive if the occur of an event does not exclude the occurrence of another event at the same time. In drawing a card from the deck of 52 cards, the occurrence of an ace card does not exclude the occurrence of a club card. Because, both identities - ace as a rank and club as a suit exist on the same card.
Figure 3: Marginal probabilities of mutually exclusive events and joint probability of mutually inclusive events in a draw of a card from the deck