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Math Help - Probability

  1. #1
    Junior Member
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    Dec 2007
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    Probability

    Hi

    The question is:

    On a six question multiple choice test there are five possible answers for each question. Only one of these answers is correct. If a student guesses randomly and independently, find the probability:

    a) being correct only on questions 1 and 4
    b) being correct on two questions only
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  2. #2
    Super Member

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    Hello,shogunhd!

    On a six-question multiple-choice test, there are five possible answers
    for each question. Only one of these answers is correct.
    If a student guesses randomly and independently, find the probability:

    a) being correct only on questions 1 and 4
    On any question: . \begin{array}{ccc} P(\text{right}) &=& \frac{1}{5} \\ P(\text{wrong}) &=&\frac{4}{5}\end{array}

    We want: .right-wrong-wrong-right-wrong-wrong

    The probability is: . \frac{1}{5}\cdot\frac{4}{5}\cdot\frac{4}{5}\cdot\f  rac{1}{5}\cdot\frac{4}{5}\cdot\frac{4}{5} \;=\;\frac{256}{15.625}



    b) being correct on two questions only
    There are: . {6\choose 2} \:=\:15 ways to choose two questions.

    P(\text{2 right}) \;=\;15\cdot\left(\frac{1}{5}\right)^2\left(\frac{  4}{5}\right)^4 \;=\;\frac{768}{3125}

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