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Over 1500 students appeared for the exam. The entrance exam has 100 multiple choice questions, each carrying 1 mark. Each question has 4 options. Due to negative marking, every incorrect choice gets –0.33 marks. Suppose 800 students choose all their answers randomly keeping uniform probability. The expected marks for 100 questions is
  • a)
    0.75
  • b)
    0.25
  • c)
    9.37
  • d)
    0.65
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Over 1500 students appeared for the exam. The entrance exam has 100 m...
The probability distribution for X is given below
Expected marks for one question, E(X) = ∑ X P (X)
= 1(0.25) + (-0.33)(0.75)
E(X) = 0.0025
Expected marks for 100 questions = 100 × 0.0025 = 0.25
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Community Answer
Over 1500 students appeared for the exam. The entrance exam has 100 m...
Understanding the Exam Structure
- The entrance exam consists of 100 multiple choice questions.
- Each question has 4 options.
- Correct answer: +1 mark
- Incorrect answer: -0.33 marks
- Unanswered questions: 0 marks
Random Guessing Scenario
- 800 students answer all questions randomly.
- The probability of choosing the correct answer: 1/4
- The probability of choosing an incorrect answer: 3/4
Calculating Expected Marks for One Question
- For a correct answer:
- Contribution = 1 * (1/4) = 0.25 marks
- For an incorrect answer:
- Contribution = -0.33 * (3/4) = -0.2475 marks
Expected Marks for One Question
- Total expected marks for one question:
- Expected marks = 0.25 - 0.2475 = 0.0025 marks
Calculating Expected Marks for 100 Questions
- Total expected marks for 100 questions:
- Expected marks for 100 questions = 100 * 0.0025 = 0.25 marks
Conclusion
- Therefore, the expected marks for a student who guesses all answers randomly is 0.25 marks, which corresponds to option 'B'. This low score reflects the impact of negative marking on random guessing.
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Over 1500 students appeared for the exam. The entrance exam has 100 multiple choice questions, each carrying 1 mark. Each question has 4 options. Due to negative marking, every incorrect choice gets –0.33 marks. Suppose 800 students choose all their answers randomly keeping uniform probability. The expected marks for 100 questions isa)0.75b)0.25c)9.37d)0.65Correct answer is option 'B'. Can you explain this answer?
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