If \( \mathrm{a} \) and \( \mathrm{b} \) are chosen randomly from t...

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If \( \mathrm{a} \) and \( \mathrm{b} \) are chosen randomly from the set consisting
\( \mathrm{P} \) of numbers \( 1,2,3,4,5,6 \) with replacement. The

W probability that \( \lim _{x \rightarrow 0}\left(\frac{a^{x}+b^{x}}{2}\right)^{2 / x}=6 \) is
(1) \( \frac{1}{2} \)
(2) \( \frac{1}{4} \)
(3) \( \frac{1}{8} \)
(4) \( \frac{1}{9} \)
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