Mutually Exclusive Events:

A set of events is mutually exclusive if the occurrence of one of them precludes the occurrence of any of other events. For example, when a pair of dice is tossed, the events 'sum of 4 occurs', 'sum of 10 occurs' and 'sum of 12 occurs' are exclusive mutually. Simply speaking, if the 2 events are mutually exclusive they cannot happen simultaneously. By using the set theoretic notation, if A₁, A₂,.. A_n be the set of mutually events then A_i Ç A_j =f for i ¹j and 1£ i, j£ n.

Independent Events

Events are independent if the occurrence or non occurrence of one does not affect occurrence or non occurrence of other. For example, when a pair of dice is tossed, the events '1^st die shows even number' and '2^nd die shows an odd number' are independent. As the outcome of 2^nd die does not affect outcome of 1^st die. It should be noted that these 2 events are not mutually exclusive as they can take place together.

Remarks

• Distinction between the mutually exclusive and independent events must be clearly made. The concept of mutually exclusive events is set theoretic in the nature while concept of independent events is probabilistic in nature.

• If 2 events A and B are mutually exclusive, they would be dependent strongly as occurrence of 1 precludes the occurrence of other.

Exhaustive Event

A set of the events is said to be exhaustive if performance of the random experiment always result in occurrence of at least 1 of them. For example, consider a ordinary pack of cards then events 'the drawn card is heart', 'the drawn card is diamond', 'the drawn card is club' and 'the drawn card is spade' is set of exhaustive event. Or we can say that all the sample points put together (that is sample space itself) would give us an exhaustive event.

If E be an exhaustive event then P(E) = 1.

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