I'm trying to find how many questions I need to study for my test

Question

The prof gave 15 questions on the study guide. Out of these 15, seven will be on the test. And out of these seven I need to answer three. How many questions do I need to study?

Answer 1

If you study 7, there are still another 8 questions from which the professor can choose 7 questions for the test and select 0 of the ones you studied. You wouldn't get your 3 correct.

If you study 8, there are still another 7 questions from which the professor can choose 7 questions for the test and select 0 of the ones you studied. You wouldn't get your 3 correct.

If you study 9, the prof can choose 6 questions you didn't study and select just 1 of the ones you studied. You wouldn't get your 3 correct.

If you study 10, the prof can choose 5 questions you didn't study and just 2 of the ones you studied. You wouldn't get your 3 correct.

If you study 11, the prof can choose 4 questions you didn't study and 3 of the ones you studied. You would get your 3 correct!

Note, these questions are not random; the professor might know which ones you are likely to study as you play the game. But if you study 11, you MUST have studied at least 3 of the 7 he choses since there are only 4 that you have not studied which can potentially be included on the test.

You have not posed a probability and statistics problem. This is arithmetic. If you want to be 90% sure that you will get 3 correct, for example, then it becomes related to probability and statistics.