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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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