Discussion
A six sided unbiased die with four green faces and two red faces is rolled seven times. Which of the following combinations is the most likely outcome of the experiment?
Answer: C
The most likely outcome is Five green faces and two red faces.
Each roll shows green with probability 2/3 and red with probability 1/3, so the number of greens in 7 rolls is binomial. The chance of \(k\) greens is proportional to \(\binom{7}{k} 2^{k}\):
| greens | 3 | 4 | 5 | 6 |
|---|---|---|---|---|
| \(\binom{7}{k} 2^{k}\) | 280 | 560 | 672 | 448 |
Five greens gives the largest value. The usual shortcut is that the most likely count of a binomial is the whole-number part of \((n + 1)p = 8 \times \frac{2}{3} = 5.33\), which is 5. Six greens is close but has fewer arrangements, and three or four greens underweight the more likely colour.
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