Two friends A and B apply for a job in the same company. The probabilities of A getting selected is…

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
  1. $\frac{8}{35}$
  2. $\frac{18}{35}$
  3. $\frac{26}{35}$
  4. $\frac{34}{35}$

Solution

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

Asked in: MHT CET 2024 (16 May Shift 2)

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