Question

Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram‟s selection is 1/6 and that of Ramesh is 1/8. What is the probability that only one of them will be selected?
1. \(\frac{{47}}{{48}}\)
2. \(\frac{1}{4}\)
3. \(\frac{{13}}{{48}}\)
4. \(\frac{{35}}{{48}}\)

Answer 1

Correct Answer - Option 2 : \(\frac{1}{4}\)

Given that,

Probability that Ram is selected ⇒ \({P_1} = \frac{1}{6}\)

Probability that Ramesh is selected ⇒ \({P_2} = \frac{1}{8}\)

Probability that only one of them is selected = P

\(\begin{array}{l} P = {P_1} \times \overline {{P_2}} + {P_2} \times \overline {{P_1}} \\ = \frac{1}{6} \times \left( {1 - \frac{1}{8}} \right) + \frac{1}{8} \times \left( {1 - \frac{1}{6}} \right)\\ = \frac{{12}}{{40}} = \frac{1}{4} \end{array}\)