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An examination paper has 150 multiple- choice questions of one mark each, with each question having four choice. Each incorrect answer fetches- 0.25 mark. Suppose 1000 students choose all their answers randomly with uniform probability. The sum total of the expected marks obtained by all these students is :
- a)0
- b)2550
- c)7525
- d)9375
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
An examination paper has 150 multiple- choice questions of one mark ea...
Let the marks obtained per question be a random variable X.
Its probability distribution table is given below:
Its probability distribution table is given below:
Expected marks per question = E(x)
Total marks expected for 150 questions = 1/16 × 150 = 75/8 marks per student
Total expected marks of 1000 students = 75/8 × 1000 = 9375 marks
So, correct answer is (D).
Most Upvoted Answer
An examination paper has 150 multiple- choice questions of one mark ea...
Understanding the Problem:
- There is an examination paper with 150 multiple-choice questions.
- Each question has four choices, and each question is worth one mark.
- For each incorrect answer, 0.25 marks are deducted.
- 1000 students choose their answers randomly with a uniform probability.
- We need to find the sum total of the expected marks obtained by all these students.
Solution:
To solve this problem, we will break it down into smaller steps:
Step 1: Calculate the probability of getting a question right or wrong:
Since each question has four choices, the probability of getting a question right is 1/4, and the probability of getting it wrong is 3/4.
Step 2: Calculate the expected marks for each question:
The expected marks for each question can be calculated by multiplying the probability of getting it right by 1 and the probability of getting it wrong by -0.25.
Expected marks = (1/4 * 1) + (3/4 * -0.25) = 0.25 - 0.1875 = 0.0625
Step 3: Calculate the expected marks for all 150 questions:
Since each question is worth one mark, the expected marks for all 150 questions will be 150 * 0.0625 = 9.375.
Step 4: Calculate the sum total of expected marks for all 1000 students:
Since each student chooses their answers randomly, the expected marks for each student will be the same, which is 9.375.
Therefore, the sum total of expected marks for all 1000 students will be 1000 * 9.375 = 9375.
Therefore, the correct answer is option 'D' - 9375.
- There is an examination paper with 150 multiple-choice questions.
- Each question has four choices, and each question is worth one mark.
- For each incorrect answer, 0.25 marks are deducted.
- 1000 students choose their answers randomly with a uniform probability.
- We need to find the sum total of the expected marks obtained by all these students.
Solution:
To solve this problem, we will break it down into smaller steps:
Step 1: Calculate the probability of getting a question right or wrong:
Since each question has four choices, the probability of getting a question right is 1/4, and the probability of getting it wrong is 3/4.
Step 2: Calculate the expected marks for each question:
The expected marks for each question can be calculated by multiplying the probability of getting it right by 1 and the probability of getting it wrong by -0.25.
Expected marks = (1/4 * 1) + (3/4 * -0.25) = 0.25 - 0.1875 = 0.0625
Step 3: Calculate the expected marks for all 150 questions:
Since each question is worth one mark, the expected marks for all 150 questions will be 150 * 0.0625 = 9.375.
Step 4: Calculate the sum total of expected marks for all 1000 students:
Since each student chooses their answers randomly, the expected marks for each student will be the same, which is 9.375.
Therefore, the sum total of expected marks for all 1000 students will be 1000 * 9.375 = 9375.
Therefore, the correct answer is option 'D' - 9375.
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An examination paper has 150 multiple- choice questions of one mark each, with each question having four choice. Each incorrect answer fetches- 0.25 mark. Suppose 1000 students choose all their answers randomly with uniform probability. The sum total of the expected marks obtained by all these students is :a)0b)2550c)7525d)9375Correct answer is option 'D'. Can you explain this answer?
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