Given: let A denote the event ‘kamal is selected’ and let B denote the event ‘vimal is selected’.
Therefore , P(A) = \(\frac{1}{3}\) and P(B) = \(\frac{1}{5}\)
Also, A and B are independent . A and not B are independent, not A and B are independent.
To Find: The probability that only one of them will be selected.
Now ,
P(only one of them is selected) = P(A and not B or B and not A)
= P(A and not B) + (B and not A)
= P(A ∩ \(\overline B\)) + P(B ∩ \(\overline A\))
= P(A) x P(\(\overline B\)) + P(B) x P(\(\overline A\))
= P(A) x [1-P(B)]+ P(B) x [1-P(A)]
= \(\frac{2}{5}\)
Therefore , The probability that only one of them will be selected is \(\frac{2}{5}\)
