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# A and B are two students.Their chances of solving a problem correctly are $\Large\frac{1}{3}$ and $\Large\frac{1}{4}$,respectively.If the probability of their making a common error is ,$\Large\frac{1}{20}$ and they obtain the same answer,then the probability of their answer to be correct is

$\begin{array}{1 1} (A)\;\frac{1}{12}\quad(B)\;\frac{1}{40}\quad (C)\;\frac{13}{20}\quad(D)\;\;\frac{10}{13}\end{array}$

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A)
Toolbox:
• If $A$ and $B$ are two events.
• $p(\overline{ A\cap B})=p(\bar{A}\cup \bar{B})$
• $p(\bar{A}\cap\bar{B})=p(\overline{A\cup B})$