# Arun and Ved appeared for an interview for two vacancies. The probability of Arun’s selection is 1/4, and that of Ved’s rejection is 2/3.

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Arun and Ved appeared for an interview for two vacancies. The probability of Arun’s selection is 1/4, and that of Ved’s rejection is 2/3. Find the probability that at least one of them will be selected.

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Given : let A denote the event ‘Arun is selected’ and let B denote the event ‘ved is selected’.

Therefore , P(A) = $\frac{1}{4}$ and P($\overline B$) = $\frac{2}{3}$ $\Rightarrow$ P(B) = $\frac{1}{3}$ and P($\overline A$) = $\frac{3}{4}$

Also, A and B are independent .A and not B are independent, not A and B are independent.

To Find: The probability that atleast one of them will get selected.

Now,

P(atleast one of them getting selected)

= P(selecting only Arun ) + P(selecting only ved) + P(selecting both)

= P(A and not B) + P (B and not A) + P (A and B)

= P( A ∩ $\overline B$) + P(B ∩ $\overline A$) + P(A ∩ B) $\frac{1}{2}$

Therefore , The probability that atleast one of them will get selected is $\frac{1}{2}$