Ans: B
$P\text{(the 2nd correct $|$ at least one correct)}$
$P\text{(the 2nd correct $|$ at least one correct)}$
$\begin{array}{cl}
= & \dfrac{P\text{(the 2nd correct and at least one correct)}}{P\text{(at least one correct)}} \\
= & \dfrac{\frac{3}{4} \times \frac{1}{3} + \frac{1}{4} \times \frac{1}{3}}{\frac{1}{4} \times \frac{2}{3} + \frac{3}{4} \times \frac{1}{3} + \frac{1}{4} \times \frac{1}{3}} \\
= & \dfrac{2}{3}
\end{array}$
