A man and his wife appear in an interview. The probability of husband‘s selection is \(\frac{1}{3}\)and the probability of wife‘s selection is  \(\frac{2}{5}\) .What is the probability that only one of them is selected?

\(\frac{7}{15}\)

Probability of man‘s selection is = \(\frac{1}{3}\)

Probability of wife ‘s selection is = \(\frac{2}{5}\)

Probability that any one of them is selected = probability of man‘s selection and not wife selection or probability of wife‘s selection not man

Then probability = \(\frac{1}{3}\) × ( 1- \(\frac{2}{5}\) ) + \(\frac{2}{5}\) × ( 1- \(\frac{1}{3}\) )

                        = \(\frac{7}{15}\)