An examination paper has 150 multiple choice questions of one mark each, with each question having four choices. Each incorrect answer fetches -0.25 marks. 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

GATE 2004 · Engineering Mathematics · Expectation · medium

Answer: 9375 (Option D)

1. Expected marks per question for one student: E[marks per question] = 1/4 - 3/16 = 4/16 - 3/16 = 1/16 = 0.0625
2. Expected marks per student (150 questions): E[per student] = 150 * (1/16) = 150/16 = 9.375
3. Total expected marks for 1000 students: Total = 1000 * 9.375 = 9375