# Homework Help: Probability student exam problem

1. Jul 12, 2010

1. The problem statement, all variables and given/known data

A class is given a list of 20 study problems from which 10 will be on an upcoming exam. If a student knows how to solve 15 of the problems, find the probability that the student will be able to answer (a) all 10 of the questions on the exam. (b) exactly 8 questions on the exam, and (c) at least 9 questions on the exam.

2. Relevant equations

3. The attempt at a solution

Well for a I found 20C10 which is the total possible combinations of questions that could be on the test then I found 20C15 which is the total number of combinations of the problems the student solved. Would you divide 20C15 by 20C10? I'm not sure how to solve this problem.

2. Jul 12, 2010

### ehild

Re: Probability

The student can solve 15 problems, but these problems are given. The student knows, which ones he can solve.
From the viewpoint of the student, there are 15 good problems and 5 wrong ones. What is the probability that all the 10 problems in the test are selected from the good ones? What is the probability, that 8 good and 2 wrong problems all selected? What is the probability that at least 9 good problems are selected?

ehild

3. Jul 12, 2010

Re: Probability

Would that be 10/15 or 1/3? because there are 10 problems being chosen and 15 good ones.

4. Jul 13, 2010

### ehild

Re: Probability

The elementary event is which problem is chosen. You said correctly already that 20C10 is the total number of the possible set of questions: you can select 10 out of 20 in (20!/10!10!) ways.
How can you select 10 question out of 15?

ehild

5. Jul 13, 2010

Re: Probability

15C10 ways?

6. Jul 13, 2010

### ehild

Re: Probability

Yes.

ehild