Question

On a multiple-choice quiz, a correct answer is awarded 4 points, but an incorrect answer costs the student 1 point. Suppose each question on the quiz has 4 choices and no question has multiple correct answers. If a student were to guess on every question, what is the number of points the student should expect to get per question?

Answer 1

Answer:

Hence, the answer is:

                $\dfrac{1}{4}$

Step-by-step explanation:

It is given that:

A correct answer is awarded 4 points, but an incorrect answer costs the student 1 point.

This means that the point +4 is added if the answer is correct.

and -1 will be added if the answer is incorrect.

Also, the probability of getting a correct answer is: 1/4

( since out of 4 choices only one option is correct)

and the probability of getting a incorrect answer is: 3/4

( since out of 4 choices 3 are incorrect)

Hence, the expected point the student should expect to get per question is:

$E(X)=\dfrac{1}{4}\times (+4)+\dfrac{3}{4}\times (-1)\\\\i.e.\\\\E(X)=1-\dfrac{3}{4}\\\\i.e.\\\\E(X)=\dfrac{1\times 4-3}{4}\\\\i.e.\\\\E(X)=\dfrac{4-3}{4}\\\\i.e.\\\\E(X)=\dfrac{1}{4}$