Question

A multiple-choice test consists of 27 questions with possible answers of a, b, c, d, e, f. Estimate the probability that with random guessing, the number of correct answers is at least 8.

Answer 1

Solution:- The probability that with random guessing, the number of correct answers is at least 8 is 0.0678.

The probability of getting correct answer by guessing = 1/6 = 0.1667

n = 27

x = 8

By applying binomial distribution:-

P(x > 8) = 1 - P(x = 0) - P(x = 1) - P(x = 2) - P(x = 3) - P(x = 4) - P(x = 5) - P(x = 6) - P(x = 7)

P(x > 8) = 1 - 0.0073 - 0.0393 - 0.1021 - 0.1703 - 0.2044 0.1881 - 0.1380 - 0.0828

P(x > 8) = 0.0678