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Kamal and Vimal appeared for an interview for two vacancies. The probability of Kamal’s selection is 1/3, and that of Vimal’s selection is 3. Find the probability that only one of them will be selected.

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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 \(\frac{2}{5}\)

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