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Math Help - Multiple choice question.

  1. #1
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    Post 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
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  2. #2
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    Re: Multiple choice question.

    Hello, rbmeee!

    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.

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

    The penalty for a wrong answer is -1.



    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

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

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

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