College Math

College Math Study Guide

4.8 Mutually Exclusive Events The nature of an event is also an essential component while working with probability. Mutually exclusive events are those events which have no common outcome. For instance, when we draw a card from a deck of 52 cards, then the event of drawing a spade is not related with another event of drawing a heart. This is because a card cannot be both spade and heart. If we wish to find the probability of these two events, then it will be found by the union of these events. The union is represented by U symbol . The Venn diagram for mutually exclusive events is given as follows: In the above diagram, Events A and B are mutually exclusive, where the occurrence of one is not influenced by the occurrence of the other. For instance, let us find the probability of two mutually exclusive events where the events are given as under: From a deck of 52 cards, what is the probability that the drawn card is A = card of spades, OR B = card of hearts? The probability in this case will be represented by the union of both events, that is, A U B: P(A U B) = n(A U B)/ n(S) Now, n(A U B) will be equal to n (A) + n (B). Thus, ( ) = ( ) + ( ) ( )

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