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Math Help - Probabilities

  1. #1
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    Probabilities

    You have a quiz with 5 questions.
    They are multiple choice with 4 possible answers for each question.

    You guess on all of them.

    1. Whats the probability you get them all wrong?
    2. Whats the probability you get them all right?
    3. Whats the probability you get at least one right?
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  2. #2
    GAMMA Mathematics
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    Quote Originally Posted by Morgan82 View Post
    You have a quiz with 5 questions.
    They are multiple choice with 4 possible answers for each question.

    You guess on all of them.

    1. Whats the probability you get them all wrong?
    2. Whats the probability you get them all right?
    3. Whats the probability you get at least one right?
    P(\text{correct}) = \frac{1}{4}
    P(\text{incorrect}) = \frac{3}{4}

    1. P(\text{incorrect})^5 = \frac{243}{1024}

    2. P(\text{correct})^5 = \frac{1}{1024}

    3. P(\text{at least one correct}) = 1 - P(\text{all incorrect}) \Rightarrow 1 - P(\text{incorrect})^5 = \frac{781}{1024}
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    GAMMA Mathematics
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    Quote Originally Posted by Plato View Post
    Recall that at least one is the opposite of none.
    I tend to write in pure math, but this is the reasoning why it looked so easy!
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