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Math Help - A test consists of 5 questions ....

  1. #1
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    A test consists of 5 questions ....

    Hi All,

    A probability problem, not sure whether this is a combination problem or permutation.

    A test consists of 5 questions. A correct answer scores 2 marks and an incorrect one, to penalize guessing, scores -1. Assuming that all the questions are answered, find probability of scoring -2.

    I figured that only way to score -2 is 1 correct and 4 incorrect, 2 - 4 = -4. All other combinations are incorrect.
    Stuck here, Can you guys give me a hint on how to proceed further? Thanks!
    Last edited by mr fantastic; March 30th 2011 at 03:31 PM. Reason: Re-titled.
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  2. #2
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    Hello, mathguy80!

    A test consists of 5 questions.
    A correct answer scores 2 marks and an incorrect one scores -1.
    Assuming that all the questions are answered, find probability of scoring -2.

    I figured that only way to score -2 is 1 correct and 4 incorrect: (1)(2) + 4(-1) = -2
    . . Right!
    Can you guys give me a hint on how to proceed further?

    I assume that the student is randomly guessing the answers,
    . . and that the probability of guessing a correct answer is \frac{1}{2}

    To get a score of -2, he must get one Correct and four Incorrect, in some order.


    There are 5 choices for the Correct answer.
    The probability that answer being correct is \frac{1}{2}

    He must get the other four equations Incorrect.
    The probability of this is: (\frac{1}{2})^4 \,=\,\frac{1}{16}


    Therefore: . P(\text{1 Correct, 4 Incorrect}) \;=\;5(\frac{1}{2})(\frac{1}{16}) \:=\:\dfrac{5}{32}

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  3. #3
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    Quote Originally Posted by mathguy80 View Post
    A test consists of 5 questions. A correct answer scores 2 marks and an incorrect one, to penalize guessing, scores -1. Assuming that all the questions are answered, find probability of scoring -2.
    I figured that only way to score -2 is 1 correct and 4 incorrect, 2 - 4 = -4.
    There are several difficulties with the statement of this question.
    It says nothing about the probability of guessing the correct answer to a given question. So let us say that \mathbf{p} is the probability that any given question is answered correctly.
    Then the probability of getting exactly one correct is \dbinom{5}{1}\mathbf{p}(1-\mathbf{p})^4 .
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  4. #4
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    Thanks @Soroban. Your answer 5/32 checks out. I hadn't made the connection that probability of guessing a correct answer is 1/2.

    @Plato, Thanks as well. This is probably an advanced idea, but allowing for variable probability of answering question correctly is very cool. Will keep this in mind for future study.
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