Discussion
Brother and sister both appear for an interview. The probability of the selection of brother is \(\frac{1}{6}\), while the probability of rejection of sister is \(\frac{3}{4}\). What is the probability that one of them is selected?
Answer: B
The probability is \(\frac{1}{3}\).
The brother is selected with probability \(\frac{1}{6}\) (rejected \(\frac{5}{6}\)); the sister is rejected with probability \(\frac{3}{4}\), so selected with \(\frac{1}{4}\). Exactly one is selected if the brother is in and the sister out, or the sister in and the brother out:
\[ \begin{aligned} \tfrac{1}{6} \times \tfrac{3}{4} + \tfrac{5}{6} \times \tfrac{1}{4} &= \tfrac{3}{24} + \tfrac{5}{24} \\ &= \tfrac{8}{24} = \tfrac{1}{3} \end{aligned} \]
\(\frac{1}{4}\) is only the sister's chance, and \(\frac{5}{6}\) only the brother's chance of rejection.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development