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Mutually Exclusive Events

Two events associated with a random experiment are said to be mutually exclusive, if both cannot occur together in the same trial. In the experiment of throwing a die, the events A = {1,4} and B = {2,5,6} are mutually exclusive events. Clearly A B = φ. Thus the sets A and B are disjoint sets. In the same experiment, the events A= {1,4} and C = {2,4,6} are not mutually exclusive because, if 4 appear on the die, then it is favorable to both events A and C. The definition of mutually exclusive events can also be extended to more than two events. We say that more than two events are mutually exclusive, if the happening of one of these, rules out the happening of all other events. The events A = {1,2}, B = {3} and C = {6}, are mutually exclusive in connection with the experiment of throwing a single die.

For example, let a pair of dice be thrown and let A, B, C be the events that the 'sum is 7', 'sum is 8', and 'sum is greater than 10' respectively.
A = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}
B = {(2,6), (3,5), (4,4), (5,3), (6,2)}
And C = {(5,6), (6,5), (6,6)}
The events A,B and C are mutually exclusive

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