Question

If a test has three multiple choice questions that offer five possible answers, determine the probability that a student will get one out of three questions correct by guessing on all of them.

• A. $\frac{49}{125}$
• B. $\frac{48}{125}$
• C. $\frac{48}{145}$
• D. $\frac{49}{145}$

Answer 1

The correct option is B $\frac{48}{125}$

Given that there are $3$ questions and each question has $5$ possible answers.

The number of possible multiple choice combinations are $5\times 5\times 5=125$

In each question , the probability of guessing correct is $\frac{1}{5}$ and probability of guessing wrong is $\frac{4}{5}$

Out of $3$ questions , the probability of getting one questions correct is ${}^3{C}_1\times {\left(\frac{4}{5}\right)}^2\times \frac{1}{5}=\frac{48}{125}$

The correct option is $B$.