A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answer just by guessing, is

Step-by-step solution

The total number of questions is n = 5 . Each question has 3 alternatives with exactly one correct answer, so the probability of guessing a correct answer is p = 1 3 and the probability of guessing an incorrect answer is q = 1 - p = 2 3 . The number of correct answers X follows a binomial distribution B(n, p) , where P(X = k) = ^ n C_ k p^ k q^ n-k . We need to find the probability of getting 4 or more correct answers, which is P(X 4) = P(X = 4) + P(X = 5) . P(X = 4) = ⁵C₄ ( 1 3 )⁴ ( 2 3 )⁵⁻⁴ = 5 1 81 2 3 = 10 243