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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 \(\frac{1}{2}\) 

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