Two friends A and B apply for a job in the same company. The probabilities of A getting selected is \(\frac{2}{5}\) and that of B is \(\frac{4}{7}\). Then the probability, that one of them is selected, is

\(\mathrm{P}(\mathrm{~A})=\frac{2}{5}, \mathrm{P}(\mathrm{~B})=\frac{4}{7}\)
Required probability
\(\begin{aligned}
& =\mathrm{P}\left(\mathrm{~A} \cap \mathrm{~B}^{\prime}\right)+\mathrm{P}\left(\mathrm{~A}^{\prime} \cap \mathrm{B}\right) \\
& =\mathrm{P}(\mathrm{~A}) \cdot \mathrm{P}\left(\mathrm{~B}^{\prime}\right)+\mathrm{P}\left(\mathrm{~A}^{\prime}\right) \cdot \mathrm{P}(\mathrm{~B})
\end{aligned}\)
\(\begin{aligned} & =\frac{2}{5}\left(1-\frac{4}{7}\right)+\left(1-\frac{2}{5}\right)\left(\frac{4}{7}\right) \\ & =\left(\frac{2}{5}\right)\left(\frac{3}{7}\right)+\left(\frac{3}{5}\right)\left(\frac{4}{7}\right) \\ & =\frac{18}{35}\end{aligned}\)