Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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.

share|improve this question
    
I believe it should be (7 chose 5)(7 choose 2)/ (12 chose 7) is this correct? –  user125627 Feb 13 at 19:24

2 Answers 2

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.

share|improve this answer
    
so you're saying it should just be (5 choose 7) / (12 choose 7)? –  user125627 Feb 13 at 6:35
    
That corresponds to choosing the solvable problems. You still have to chose the not solvable problems. –  Kai Sikorski Feb 13 at 6:40
    
Okay. hm.. would that be (2 choose 0) because there will be 2 other problems that you can't solve? –  user125627 Feb 13 at 6:43

In order for the student to solve exactly $5$ problems out of the $7$, the exam must contain exactly $5$ out of the $7$ problems the student knows how to solve, and exactly $2$ of the other three problems.

How many different combinations are there?

share|improve this answer
    
Could you explain why you said "exactly 2 of the other three problems"? I understand the 5 out of 7 but I feel like I am missing the other half. My professor told me that the top if summed together should equal the denominator. –  user125627 Feb 13 at 17:15
    
@user125627 Is the student gets exactly $5$ of $7$ questions right, what does he do on the other two? –  N. S. Feb 14 at 2:24

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.