The Most Random Random Quiz

Let's say that hypothetically, you wanted to create a random quiz which seemed to change completely every time you took it. So, if you were to take the quiz twice, there would be a greater than 50% chance that all questions would be different the second time around. If the quiz will show twenty questions at a time, how many total questions will there need to be?

Well lets begin by first imagining that there are forty total questions. the odds of any one answer having never appeared before would be 1/2. However, for the next answer, the odds would instead be 19/39, because the questions cannot be the one we already chose. Then the next one would be 18/38, 17/37, etc. To find the odds of all of this, you multiply all those fractions together and find that there is about a 0.0000000007 percent chance of you getting all new answers.

So what if there were instead 100 possible questions. Well if we do the same thing we find that there is now a 0.07 percent chance of getting all new answers.

We're getting there...

So lets skip ahead to 500 questions. You would still only have a 43.5% chance of getting all different answers. Definitely closer.

What about 600? Then you have about a 50.2% chance, so then...

You need at least 597 questions to have a fifty percent chance of getting different questions both times. Unfortunately the Jetpunk question limit is 500 so this is not possible. I hope 43.5% is satisfactory.

So if you ever take a random quiz twice and notice repeated answers, it's not because the quiz maker is lazy, it's just mathematically probable.