If `E_1, E_2, .... , E_n` are n events associated with an experiment whose sample space is S and if `E_1 cup E_2 cup E_3 cup ...... cup E_n = underset (i= 1) (overset (n) cupE_i) = S`
then `E_1, E_2, ...... , E_n` are called exhaustive events. In other words, events `E_1, E_2, ...... , E_n`, are said to be
exhaustive if atleast one of them necessarily occurs whenever the experiment is performed.
Further, if `E_i E_j = phi` for `i nej` i.e. , events `E_i` , and `E_j` are pairwise disjoint and ,`underset (i= 1) (overset (n) cupE_i)` then events `E_1, E_2, .... , E_n` are called mutually exclusive and exhaustive events.
e.g.
For three events "A", "B" and "C" which are mutually exclusive and exhaustive, the probability that atleast one of the events would occur i.e. the probability of the occurrence of the union of the events is a certainty and is given by the sum of the probabilities of the individual events.
`P(A ∪ B ∪ C) = 1` [Exhaustive]
`P(A ∪ B ∪ C) = P(A) + P(B) = 1` [Mutually Exclusive and Exhaustive]
If `E_1, E_2, .... , E_n` are n events associated with an experiment whose sample space is S and if `E_1 cup E_2 cup E_3 cup ...... cup E_n = underset (i= 1) (overset (n) cupE_i) = S`
then `E_1, E_2, ...... , E_n` are called exhaustive events. In other words, events `E_1, E_2, ...... , E_n`, are said to be
exhaustive if atleast one of them necessarily occurs whenever the experiment is performed.
Further, if `E_i E_j = phi` for `i nej` i.e. , events `E_i` , and `E_j` are pairwise disjoint and ,`underset (i= 1) (overset (n) cupE_i)` then events `E_1, E_2, .... , E_n` are called mutually exclusive and exhaustive events.
e.g.
For three events "A", "B" and "C" which are mutually exclusive and exhaustive, the probability that atleast one of the events would occur i.e. the probability of the occurrence of the union of the events is a certainty and is given by the sum of the probabilities of the individual events.
`P(A ∪ B ∪ C) = 1` [Exhaustive]
`P(A ∪ B ∪ C) = P(A) + P(B) = 1` [Mutually Exclusive and Exhaustive]