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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.

Answers (1)

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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, 

A \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.

Posted by

HARSH KANKARIA

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