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Math Help - Probability of passing a quiz

  1. #1
    Member oldguynewstudent's Avatar
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    Probability of passing a quiz

    An instructor gave her students 12 problems, telling them that 3 of the problems will be on a quiz and that passing the quiz requires solving all 3 of the problems.

    a) Given that the instructor chooses the 3 problems at random, what is the probability for a student who knows only 10 problems to pass?

    I calculate that the student has 10/12 chances to know the first problem, 9/11 to know the second, and 8/10 to know the third. Therefore the student's probability of passing the quiz is (10/12)*(9/11)*(8/10)= .545

    b) What are the chances to fail for a student who knows only 8 problems.

    That student has 1 - (8/12)*(7/11)*(6/10) = .745 probability of failing.

    Are these answers correct?
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  2. #2
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    Right.

    Another way to approach the first problem: There are \binom{12}{3} ways for the instructor to pick the 3 problems, all of which are equally likely. In \binom{10}{3} of these cases, the student knows all 3. So...
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