Tutorial Not Mutually Exclusive Events


Not Mutually Exclusive Events


   


Two events are called not mutually exclusive if they have al least one outcome common between them. If the two eventsA andB are not mutually exclusive events, thenA intersection B is not     equal to empty set. Similarly, A, BandC are not mutually exclusive events ifA intersection B     intersection C is not equal to empty set. Thus they must have at least one common point between them. Consider a sample space:



Let and
Here
Thus,A intersection B is not equal to empty set i.e.A intersection B exist. HereA andB are not mutually exclusive events.A intersection B consists of outcomes which are common to both A andB. As shown in the figure a Vann diagram in which A andB are not mutually exclusive events. Some area underA is common withB. If the eventAis a part of the eventB, then A intersection B is equal to     A.. This is shown in the figure:






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