Event - Mutually Exclusive Events


  • Types of Event - Mutually Exclusive Events


In the experiment of rolling a die, a sample space is S = {1, 2, 3, 4, 5, 6}. Consider events, A ‘an odd number appears’ and B ‘an even number appears’ Clearly the event A excludes the event B and vice versa. In other words, there is no outcome which ensures the occurrence of events A and B simultaneously. Here
A = {1, 3, 5} and B = {2, 4, 6} 
Clearly A ∩ B = φ,  i.e., A and B are disjoint sets. 
In general, two events A and B are called mutually exclusive events if the occurrence of any one of them excludes the occurrence of the other event, i.e., if they can not occur simultaneously. In this case the sets A and B are disjoint. 
Again in the experiment of rolling a die, consider the events A ‘an odd number appears’ and event B ‘a number less than 4 appears’ 
Obviously A = {1, 3, 5} and B = {1, 2, 3} 
Now 3 ∈ A  as well as 3 ∈ B 
Therefore,  A and B are not mutually exclusive events.
Remark:  Simple events of a sample space are always mutually exclusive.
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