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 \(\frac{1}{2}\)
