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Three coins are tossed. Describe (ii) Three events which are mutually exclusive and exhaustive.

5.   Three coins are tossed. Describe

   (ii) Three events which are mutually exclusive and exhaustive.

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Sample space when three coins are tossed = [Sample space when a coin is tossed thrice!]

S = {HHH, HHT, HTH, HTT, THH, TTH, THT, TTT}

Let ,

A = Getting no tails = {HHH}

B = Getting exactly one tail = {HHT, HTH, THH}

C = Getting at least two tails = {HTT, THT, TTH}

Clearly, A  \cap  B  = \phi ; B  \cap  C = \phi ; C  \cap  A  = \phi

Since (A and B), (B and C) and (A and C) are mutually exclusive

Therefore A, B and C are mutually exclusive.

Also, 

\cup B \cup C = S

Hence A, B and C are exhaustive events.

Hence, A, B and C are three events which are mutually exclusive and exhaustive.

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