A student prepares for an exam by studying a list of 12 problems. She can solve 9 of them. For the exam, the instructor selects 7 problems at random from the 12 on the list given to the students. What is the probability that the student can solve 5 of the 7 problems on the exam?
I am really confused by this problem. My first initial thought was to do:
(5 chose 7)(7 chose 0)/ (12 chose 7)
I am not 100% sure about this though.
Best Answer
Your denominator is right. That's the total number of possible exams. In the numerator you want the total number of exams where the student can solve 5/7 problems. So you want to chose the set of solvable problems and then chose the set of not solvable problems.