Question

A test has three multiple choice questions that offer five possible answers. Draw a tree diagram that shows all the possible multiple-choice combinations for the answers to the test and determine the probability that a student will get two out of three questions correct by guessing on all of them.

• A. $\frac{12}{125}$
• B. $\frac{16}{125}$
• C. $\frac{12}{145}$
• D. $\frac{16}{145}$

Answer 1

The correct option is A $\frac{12}{125}$

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 two questions correct is ${}^3{C}_2\times {\left(\frac{1}{5}\right)}^2\times \frac{4}{5}=\frac{12}{125}$