Question

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

(a) \(\frac{17}{3^5}\)

(b) \(\frac{13}{3^5}\)

(c) \(\frac{11}{3^5}\)

(d) \(\frac{10}{3^5}\)

Answer 1

(c) \(\frac{11}{3^5}\)

Probability of guessing a correct answer = \(\frac{1}{3}\)

Probability of guessing an incorrect answer = \(\frac{2}{3}\)

∴ Probability of guessing 4 or more correct answers 

= ⁵C₄ \(\big(\frac{1}{3}\big)^4\)\(\big(\frac{2}{3}\big)\) + ⁵C₅ \(\big(\frac{1}{3}\big)^5\) = 5 x \(\frac{2}{3^5}\) + \(\frac{1}{3^5}\) = \(\frac{11}{3^5}\).