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Math Help - Challenging probability question

  1. #1
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    Challenging probability question

    The probability that a student passes an exam is 1/3. If 5 people took the exam, what is the probability that only 4 of them pass?

    A. (1/3)^5
    B. 4(2/3)^4 * 4(1/3)
    C. 4(1/3)^4 * (2/3)
    D. (2/3)^5
    E. 5(1/3)^4 * (2/3)
    F. None of the above

    Can someone post up what the answer is and an explanation for this?
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  2. #2
    MHF Contributor matheagle's Avatar
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    I assume you mean EXACTLY 4 of 5.
    This is a binomial rv with n=5 and p=1/3...  {5\choose 4} \biggl({1\over 3}\biggr)^4 \biggl({2\over 3}\biggr)^1.
    So, E is correct.
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