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Math Help - Counting Techniques.

  1. #1
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    Counting Techniques.

    An exam consists of 10 multiple choice questions (each question with 3 choices). If a student guesses at every answer, what is the pobability that he/she will get 6 questions correct?

    Is the correct answer C(10,6)/3^10? Or .36%?

    Please let me know if I'm making a mistake here.
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  2. #2
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    Quote Originally Posted by jebckr View Post
    An exam consists of 10 multiple choice questions (each question with 3 choices). If a student guesses at every answer, what is the pobability that he/she will get 6 questions correct?

    Is the correct answer C(10,6)/3^10? Or .36%?

    Please let me know if I'm making a mistake here.
    X ~ Binomial(n = 10, p = 1/3).

    \Pr(X = 6) = ^{10}C_6 \left( \frac{1}{3} \right)^6 \left( 1 - \frac{1}{3} \right)^{10 - 6}.
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  3. #3
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    So it's 5.66%?
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  4. #4
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    Quote Originally Posted by jebckr View Post
    So it's 5.66%?
    Well, if you have pressed the correct buttons on your calculator then I suppose this would be the correct answer (expressed as a percentage. Personally, expressing probabilities such as this as a percentage is something I do not like. But that's just me).
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