A man and his wife appear in an interview of two vacancies in the same post. The probability of the husband's selections $$\frac{1}{7}$$ and the probability of the wife's selections $$\frac{1}{5}$$. What is the probability that only one of them is selected?

Let A = Event that husband is selected and B = Event that wife is selected.

=> $$P(A)=\frac{1}{7}$$ and $$P(\overline A)=1-\frac{1}{7}=\frac{6}{7}$$

Similarly, $$P(B)=\frac{1}{5}$$ and $$P(\overline B)=1-\frac{1}{5}=\frac{4}{5}$$

$$\therefore$$ Probability that only one is selected = $$P(A)\times P(\overline B)+$$ $$P(B)\times P(\overline A)$$

= $$(\frac{1}{7}\times\frac{4}{5})+(\frac{1}{5}\times\frac{6}{7})$$

= $$\frac{4}{35}+\frac{6}{35}$$

= $$\frac{10}{35}=\frac{2}{7}$$