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Math Help - i hate probabilities please help :)

  1. #1
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    i hate probabilities please help :)

    An instructor gives his class a set of 11 problems and announces that the next quiz will consist of a random selection of 5 of them. If a student has figured out how to answer 6 of the problems correctly, what is the probability the he or she will answer correctly:
    (a) All 5 problems?
    (b) At least 4 problems?
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  2. #2
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    Hello, asugirl87!

    An instructor gives his class a set of 11 problems and announces
    that the next quiz will consist of a random selection of 5 of them.
    If a student has figured out how to answer 6 of the problems correctly,
    what is the probability the he or she will answer correctly:
    (a) All 5 problems?

    There are: {11\choose5} \,=\,462 possible quizzes.

    There are {6\choose5} = 6 ways that the five questions are among the six the student knows.

    Therefore: . P(\text{5 right}) \:=\:\frac{6}{462} \:=\:\frac{1}{77}



    (b) At least 4 problems?

    "At least four" means 4 or 5 right.

    There are {6\choose4} = 15 ways that four questions are among the six the student knows.

    There are 6 ways that all five questions are among the six the student knows.

    Hence, there are: .  16 + 6 \,=\,21 ways to get 4 or 5 right.

    Therefore: . P(\text{4 or 5 right}) \:=\:\frac{21}{462} \:=\:\frac{1}{22}

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