Ajay and his wife Reshmi appear in an interview for two vaccancies in the same post. The Probability of Ajay's selection is 1/7 and that of his wife Reshmi's selection is 1/5. What is the probability that only one of them will be selected?

P( only one of them will be selected) = p[(E and not F) or (F and not E)] 

 =  $PE\cap F\cup F\cap E$ 

=  $PEPF+PFPE$

 = $\frac{1}{7}\times \frac{4}{5}+\frac{1}{5}\times \frac{6}{7}=\frac{2}{7}$