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

Hence, the answer is:

`(1)/(4)`

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)=(1)/(4)* (+4)+(3)/(4)* (-1)\\\\i.e.\\\\E(X)=1-(3)/(4)\\\\i.e.\\\\E(X)=(1* 4-3)/(4)\\\\i.e.\\\\E(X)=(4-3)/(4)\\\\i.e.\\\\E(X)=(1)/(4)`