# 5 essays, two chosen, one chosen probability 1

1. Oct 10, 2012

### LifeSuks

That title may be kind of obscure.
Say you are given three essays to study for a test. You know that, on test day, two of these essays wil be provided from which you may choose one to write about. I'm sure all of your are familiar with this style. If you choose two to study, then, come test day, the probability of at least one of those that you chose will show up is 1.

Now, what if you are given five prompts from which to choose, two (I think) of which will be provided on the test day, and of which, again you choose 1 to write about? What is the minimum number of prompts that you must study to ensure that at least one shows up on the day of the test?

I know this should be really easy but I'm confused.

BTW, if you don't mind, we might as well derive the general result, which I'm not totally sure how to define without sounding like an idiot.

2. Oct 10, 2012

### haruspex

If you are given N to study and come the test you have to choose one of a subset of R, will studying N-R be enough? What do you think?

3. Oct 11, 2012

### mathman

N-R+1 should do.