Comprehension
Ms. Banerjee has carefully studied chances of her school winning each of the competitions. Based on in-depth calculations, she realized that her school is quite likely to win district level competition but has low chances of winning the international competition. She listed down the following probabilities of wins for different competitions. Prize was highest for international competition and lowest for district level competition (in that order).
Competition Probabilities
| Competition | Probability of win |
|---|---|
| District | 0.95 |
| State | 0.60 |
| National | 0.10 |
| International | 0.05 |
All the students are studying in the school for the last twelve years. She wanted to select the best team for all four competitions (Ms. Banerjee had no other information to select students).
Question: 1
Which of three members should form the team for the International competition?
Which of three members should form the team for the International competition?
Show Hint
When a contest is very hard to win, choose members with the highest {upside} (peak scores), not just the highest averages—peaks win tournaments, averages win leagues.
Updated On: Dec 4, 2025
- 4, 11, 14
- 2, 8, 14
- 1, 6, 12
- 13, 14, 15
- 1, 3, 4
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The Correct Option is B
Solution and Explanation
Idea. For the International competition the win probability is very low (0.05), so to maximize the small chance of winning we should prioritize students with the highest peak performance (most 100% scores), rather than the highest average (which rewards consistency more than spikes).
Step 1: Rank by number of 100% scores.
From the table (out of 100 tests each): - \#14: 20, \#2: 15, \#8: 12, \#6: 10, \#3/\#10: 8, \#1: 7, \#5/\#12: 6, ...
Step 2: Pick top three.
Top three peak performers are students 14 (20), 2 (15), and 8 (12).
\[ \boxed{\text{International team: Students 2, 8, 14}} \]
Step 1: Rank by number of 100% scores.
From the table (out of 100 tests each): - \#14: 20, \#2: 15, \#8: 12, \#6: 10, \#3/\#10: 8, \#1: 7, \#5/\#12: 6, ...
Step 2: Pick top three.
Top three peak performers are students 14 (20), 2 (15), and 8 (12).
\[ \boxed{\text{International team: Students 2, 8, 14}} \]
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Question: 2
Which of the following members should constitute the team for the district level competition?
Which of the following members should constitute the team for the district level competition?
Show Hint
When probability of success is high (like district level), it's best to assign weaker candidates there and preserve stronger candidates for tougher contests.
Updated On: Mar 20, 2026
- 4, 11, 14
- 1, 4, 11
- 4, 5, 6
- 4, 11, 13
- Any team can win the competition
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The Correct Option is D
Solution and Explanation
Step 1: Probability of winning at district level.
The probability of winning the district competition is very high at 0.95. This means even average-performing students can secure a win. Hence, the selection for district level does not require the very best students.
Step 2: Reserve strong candidates for higher-level competitions.
Since the international and national competitions have much lower probabilities of winning, the strongest students (like 2, 8, 14 for international and 1, 3, 6 for national) should be reserved for those.
Step 3: Choose weaker performers for district level.
Students 4, 11, and 13 all have average = 70 but very low cent-per-cent scores (1, 1, and 2 respectively). Their consistency is decent, but they lack the peak brilliance of others. This makes them ideal for the district team since even average performance can secure the win. \[ \boxed{\text{District team: Students 4, 11, 13}} \]
The probability of winning the district competition is very high at 0.95. This means even average-performing students can secure a win. Hence, the selection for district level does not require the very best students.
Step 2: Reserve strong candidates for higher-level competitions.
Since the international and national competitions have much lower probabilities of winning, the strongest students (like 2, 8, 14 for international and 1, 3, 6 for national) should be reserved for those.
Step 3: Choose weaker performers for district level.
Students 4, 11, and 13 all have average = 70 but very low cent-per-cent scores (1, 1, and 2 respectively). Their consistency is decent, but they lack the peak brilliance of others. This makes them ideal for the district team since even average performance can secure the win. \[ \boxed{\text{District team: Students 4, 11, 13}} \]
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Question: 3
Ms. Banerjee has to select the team for national competition after she has selected the team for international competition. A student selected for international competition cannot be a part of national competition. Which is the best team for the national competition?
Ms. Banerjee has to select the team for national competition after she has selected the team for international competition. A student selected for international competition cannot be a part of national competition. Which is the best team for the national competition?
Show Hint
When choosing for competitions with moderately low probability of success (like nationals), a mix of consistency (high averages) and occasional brilliance Cent-per-cent spikes) gives the best winning chance.
Updated On: Dec 4, 2025
- 1, 7, 4
- 8, 9, 10
- 2, 8, 14
- 3, 6, 1
- Any of remaining students, as it would not matter
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Exclusion of international team.
From Q33, the international team was chosen as \{2, 8, 14\}. These students are no longer eligible for the national competition.
Step 2: Strategy for national competition.
The probability of winning the national contest is only 0.10 (low, but higher than international). To maximize chances, the team should still balance both average performance Consistency) and peak performance (number of cent-per-cent scores).
Step 3: Candidate pool after exclusion.
Remaining high performers Based on averages and cent-per-cent scores): - Student 1: Avg = 70, Cent = 7
- Student 3: Avg = 65, Cent = 8
- Student 6: Avg = 65, Cent = 10
Other students (like 4, 7, 9, 10, 11, 12, 13, 15) have lower peak or less consistency compared to these three.
Step 4: Best team selection.
Students 1, 3, and 6 together provide: - High averages (65–70 rang(E).
- Strong cent-per-cent spikes (7–10 times).
This maximizes the chance of outperforming at the national level.
\[ \boxed{\text{National team: Students 3, 6, 1}} \]
From Q33, the international team was chosen as \{2, 8, 14\}. These students are no longer eligible for the national competition.
Step 2: Strategy for national competition.
The probability of winning the national contest is only 0.10 (low, but higher than international). To maximize chances, the team should still balance both average performance Consistency) and peak performance (number of cent-per-cent scores).
Step 3: Candidate pool after exclusion.
Remaining high performers Based on averages and cent-per-cent scores): - Student 1: Avg = 70, Cent = 7
- Student 3: Avg = 65, Cent = 8
- Student 6: Avg = 65, Cent = 10
Other students (like 4, 7, 9, 10, 11, 12, 13, 15) have lower peak or less consistency compared to these three.
Step 4: Best team selection.
Students 1, 3, and 6 together provide: - High averages (65–70 rang(E).
- Strong cent-per-cent spikes (7–10 times).
This maximizes the chance of outperforming at the national level.
\[ \boxed{\text{National team: Students 3, 6, 1}} \]
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