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. $\frac{10}{3^5}$
• B. $\frac{17}{3^5}$
• C. $\frac{13}{3^5}$
• D. $\frac{11}{3^5}$

Answer 1

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

Probability of getting a correct answer$=\frac{1}{3}$

Probability of getting an incorrect answer$=1-\frac{1}{3}=\frac{3-1}{3}=\frac{2}{3}$

$\therefore$ Probability of getting $4$ or more correct answers is

$=5_{c_4}{\left(\frac{1}{3}\right)}^4\left(\frac{2}{3}\right)+5_{c_5}{\left(\frac{1}{3}\right)}^5$

$=5\times \frac{2}{3^5}+\frac{1}{3^5}$

$=\frac{1}{3^5}(10+1)$

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