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In an examination, the probability of a candidate solving a question is $\frac{1}{2}$. Out of given 5 questions in the examination, what is the probability that the candidate was able to solve at least 2 questions?
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$\frac{13}{16}$
$\begin{aligned} & P={ }^{5} C_{2}\left(\frac{1}{2}\right)^{2}\left(\frac{1}{2}\right)^{3}+{ }^{5} C_{3}\left(\frac{1}{2}\right)^{3}\left(\frac{1}{2}\right)^{2} \\ &+{ }^{5} C_{4}\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{1}+{ }^{5} C_{5}\left(\frac{1}{2}\right)^{5}\left(\frac{1}{2}\right)^{0} \\ &=\left(\frac{1}{2}\right)^{5}\left[{ }^{5} C_{2}+{ }^{5} C_{3}+{ }^{5} C_{4}+{ }^{5} C_{5}\right] \\ &=\frac{1}{3^{2}}[10+10+5+1] \\ &=\frac{1}{3^{2}} \times 26=\frac{13}{16} \end{aligned}$
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