Ans: (a) (i) $\dfrac{28}{45}$ (ii) $\dfrac{16}{45}$ (iii) $\dfrac{44}{45}$ (b) (i) Betty (ii) Alice
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- The required probability
$\begin{array}{cl}
= & \dfrac{C^8_2}{C^{10}_2} \\
= & \dfrac{28}{45}
\end{array}$ - The required probability
$\begin{array}{cl}
= & \dfrac{C^2_1C^8_1}{C^{10}_2} \\
= & \dfrac{16}{45}
\end{array}$ - The required probability
$\begin{array}{cl}
= & \dfrac{28}{45} + \dfrac{16}{45} \\
= & \dfrac{44}{45}
\end{array}$
- The required probability
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- The mean result of Alice
$\begin{array}{cl}
= & \dfrac{279 + 280 + \cdots + 265}{10} \\
= & 275\text{ s}
\end{array}$The mean result of Betty
$\begin{array}{cl}
= & \dfrac{272 + 269 + \cdots + 272}{10} \\
= & 272 \text{ s}
\end{array}$Since the mean result of Betty is better than that of Alice, then Betty is likely to get a better result.
- According to the past experience, Alice has $3$ out of $10$ results that faster than the best record. However, Betty has only $1$ out of $10$ results that faster than the best record. Therefore, Alice has a greater chance of breaking the record.
- The mean result of Alice
