An examination paper has 150 multiple-choice questions of one mark each, with…
2004
An examination paper has 150 multiple-choice questions of one mark each, with each question having four choices. 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
Attempted by 3 students.
Show answer & explanation
Correct answer: D
Solution: Compute the expected marks step by step.
Probability of a correct answer = 1/4; probability of an incorrect answer = 3/4.
Expected marks per question = (1/4)*1 + (3/4)*(-0.25) = 1/16 = 0.0625.
Expected marks per student for 150 questions = 150 * (1/16) = 150/16 = 9.375.
Total expected marks for 1000 students = 1000 * 9.375 = 9375.
Answer: 9375