In a multiple-choice examination, there are 10 questions with one correct option out of 4 options for each question. A student gets 4 marks for each correct answer and 1 mark is deducted for each incorrect answer. The probability that a student, guessing randomly on every question, scores 30 marks in this exam is...

Step-by-step solution

Let x be the number of correct answers and y be the number of incorrect answers. x + y = 10 The total marks scored is given by 4x - y = 30 . Substituting y = 10 - x , we get: 4x - (10 - x) = 30 5x = 40 x = 8 The student must answer exactly 8 questions correctly and 2 questions incorrectly. The probability of guessing a correct answer is p = 1 4 and an incorrect answer is q = 3 4 . Using binomial distribution, the probability of getting exactly 8 correct answers is: P(X = 8) = ¹⁰C₈ ( 1 4 )⁸ ( 3 4 )² P(X = 8) = 45 1