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# Three coins are tossed. Describe (iv) Two events which are mutually exclusive but not exhaustive.

5.  Three coins are tossed. Describe

(iv) Two events which are mutually exclusive but not 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 exactly one head = {HTT, THT, TTH}

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

Clearly, A  $\cap$  B  = $\phi$

Hence, A and B are mutually exclusive.

Also, A  $\cup$  B  $\neq$ S

Hence, A and B are not exhaustive.

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