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

The correct option is C $\frac{11}{3^5}$

Probability that answer is correct, $p=\frac{1}{3}$
Probability that answer is not correct, $q=1-p=\frac{2}{3}$
Probabilty of getting $4$ or more correct answers $={}^5{C}_4{\left(\frac{1}{3}\right)}^4\cdot \frac{2}{3}+{}^5{C}_5{\left(\frac{1}{3}\right)}^5$
$=5\cdot \frac{2}{3^5}+\frac{1}{3^5}$
$=\frac{11}{3^5}$