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Homework Help: Determining probability using combinations/permutations (i think)

  1. Feb 4, 2009 #1
    1. The problem statement, all variables and given/known data
    a student has an exam, the teacher gives 30 questions and 10 of the 30 will be on the final exam. if the student knows how to solve 25 of the 30, what is:
    a) the probability he will get perfect
    b) the probability he will get at least 8 questions right

    2. Relevant equations
    permutations and combinations

    3. The attempt at a solution
    for part a i have:
    sample space= 30Choose10= 30045015
    to get all 10 questions right, the 10 questions on the exam must be within the 25 he knows how to do- 25choose10= 3268760. to find the probability i did: 3268760/30045015= 0.1087.
    i dont think this is right because it seems too low and since he knows most of the questions i would expect the probability to be higher.

    for part b: i use the same sample space of 30choose10, but im stuck on the "at least 8 questions right part"

    any help for this would be appreciated
  2. jcsd
  3. Feb 4, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    You've got the first one right. Yeah, it seems kind of low, but then he only knows how to solve 'most of them'. And he has to get 10 right in a row. It's not that unreasonable. For the second one what's the probability he gets 9 questions right and 1 wrong and what's the probability he get 8 right and 2 wrong. Then add those two to the probability from the first question.
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