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 answers 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

Answer: (C)

$\frac{11}{ 3^5}$

Answer 2

Probability of guessing a correct answer, $p = \frac{1}{3}$ and probability of guessing a wrong answer, q = 2/3
$\therefore$The probability of guessing a 4 or more correct answers
$^5 C _4 \bigg(\frac{1}{3} \bigg)^4 . \frac{2}{3}+ ^5 C _5 \bigg(\frac{1}{3} \bigg)^5 = 5.\frac{2}{3^5}+\frac{1}{3^5}= \frac{11}{3^5}$