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Exhaustive Events

Consider the experiment of throwing a die. We have S = {1, 2, 3, 4, 5, 6}. Let us define the following events

A: 'a number less than 4 appears',
B: 'a number greater than 2 but less than 5 appears' and
C: 'a number greater than 4 appears'.

Then A = {1, 2, 3}, B = {3,4} and C = {5, 6}. We observe that
A B C = {1, 2, 3} {3, 4} {5, 6} = S.
Such events A, B and C are called exhaustive events. In general, if E1, E2, ..., En are n
events of a sample space S and if
E1 E2 E3 ... En = = S
then E1, E2, ...., En are called exhaustive events. In other words, events E1, E2, ..., En
are said to be exhaustive if atleast one of them necessarily occurs whenever the experiment is performed.
Further, if Ei Ej = φ for i j i.e., events Ei and Ej are pair wise disjoint and, = S,
then events E1, E2, ..., En are called mutually exclusive and exhaustive events.

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