# Multiple choice question.

• Oct 15th 2011, 08:11 AM
rbmeee
Multiple choice question.
A multiple choice question has 4 options. Choosing the correct option gives a student 3 marks.Choosing the wrong answer incurs negative marks so if a student chooses an option randomly,his expected score is zero.Suppose the student has successfully eliminated 2 incorrect options his expected score if he chooses randomly among the remaining option is:-
1
1.5
0
3
• Oct 15th 2011, 05:38 PM
Soroban
Re: Multiple choice question.
Hello, rbmeee!

Quote:

A multiple-choice question has 4 options.
Choosing the correct option gives a student 3 marks.
Choosing the wrong answer incurs negative marks.
So if a student chooses an option randomly, his expected score is zero.

$\displaystyle E \;=\;\tfrac{1}{4}(+3) + \tfrac{3}{4}(x) \:=\:0 \quad\Rightarrow\quad x \,=\,-1$

The penalty for a wrong answer is -1.

Quote:

Suppose the student has successfully eliminated 2 incorrect options.
His expected score, if he chooses randomly among the remaining option, is:

. . (a) 1 . . (b) 1.5 . . (c) 0 . . (d) 3

. . $\displaystyle \begin{Bmatrix} P(\text{right}) &=& \tfrac{1}{2} \\ \\[-3mm] P(\text{wrong}) &=& \frac{1}{2} \end{Bmatrix}$

$\displaystyle E \;=\;\tfrac{1}{2}(+3) + \tfrac{1}{2}(-1) \;=\;1\;\;\text{ answer (a)}$