Two nos are selected at random from the first 20 natural number . Find the probability in which bith are prime

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{Prime} \mathrm{numbers} \mathrm{between} 1 \mathrm{and} 20 \mathrm{are} 2,3,5,7,11,13,17,19\to 8 \mathrm{numbers} \\ \mathrm{Hence} \mathrm{required} \mathrm{probability}=\frac{{ }^8{\mathrm{C}}_2}{{ }^{20}{\mathrm{C}}_2} \\ =\frac{{\displaystyle \frac{8\times 7}{2\times 1}}}{{\displaystyle \frac{20\times 19}{2\times 1}}} \\ =\frac{8\times 7}{20\times 19} \\ =\frac{14}{95} \end{gathered}$$

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