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Math Help - True or False Probability

  1. #1
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    True or False Probability

    Wheeewe; this wears me out......
    A test consists of 10 true/false questions. To pass the test a student must get 60% or better on the test (Answer 6 or more questions correctly). If a student randomly guesses, what is the probability that the student will pass the test?
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  2. #2
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    Hello, Allenge!

    A test consists of 10 true/false questions.
    To pass the test a student must get 60% or better on the test.
    If a student randomly guesses, what is the probability that he/she will pass the test?

    The student must get: .6 right or 7 right or 8 right or 9 right or 10 right.

    We have: . P(\text{Right}) = \tfrac{1}{2},\;P(\text{Wrong}) = \tfrac{1}{2}


    We work out the separate probabilities . . .

    . \begin{array}{cccc}\text{6R, 4W} & {10\choose6}(\frac{1}{2})^6(\frac{1}{2})^4 &=& \frac{210}{1024} \\ \\[-4mm]<br /> <br />
\text{7R, 3W} & {10\choose7}(\frac{1}{2})^7(\frac{1}{2})^3 &=& \frac{120}{1024} \\ \\[-4mm]<br /> <br />
\text{8R, 2W} & {10\choose8}(\frac{1}{2})^8(\frac{1}{2})^2 &=& \frac{45}{1024} \\ \\[-4mm]<br /> <br />
\text{9R, 1W} & {10\choose9}(\frac{1}{2})^9(\frac{1}{2})^1 &=& \frac{10}{1024} \end{array}
    \begin{array}{cccccc}\text{10R, 0W} & {10\choose10}(\frac{1}{2})^{10}(\frac{1}{2})^0 &=& \frac{1}{1024}<br />
\end{array}

    and add: . P(\text{pass}) \:=\:\tfrac{210}{1024} + \tfrac{120}{1024} + \tfrac{45}{1024} + \tfrac{10}{1024} + \tfrac{1}{1024} \;=\;\tfrac{386}{1024} \:=\:\frac{193}{512}<br /> <br />

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