Probability student exam problem

[themadhatter1]

Homework Statement

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.

Homework Equations

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.

 

[ehild]

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

 

[themadhatter1]

What is the probability that all the 10 problems in the test are selected from the good ones?
ehild

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

 

[ehild]

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

 

[themadhatter1]

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

₁₅C₁₀ ways?

 

[ehild]

Yes.

ehild