# 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.

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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 $\frac{2}{5}$