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

5.  Three coins are tossed. Describe

(v) Three 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 tail = {HHT, HTH, THH}

B = Getting exactly two tails = {HTT, TTH, THT}

C = Getting exactly three tails = {TTT}

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 = {HHT, HTH, THH, HTT, TTH, THT, TTT} $\neq$ S

Hence A, B and C are not exhaustive events.

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