# Probability of homework being graded?

Say you have a class with 15 assignments. Over the course of the semester the teacher randomly choses 5 assignments to grade.

The teacher also wants to keep it a surprise, that means the first assignment to be graded can't be assignment 11. Because then you would know that assignments 12, 13, 14, and 15 will be graded.

If you have already turned in some assignments, what would be the chance of todays assignment being graded? Say assignments 2, 5, and 7 have been graded already. What would the chance be that assignment 8 would be graded?

There seems to be some unexpected hanging type paradox embedded in this question which hasn't really had a consensus on a resolution, for at least the last homework assigned, so I will tentatively ignore the surprise condition.

Assuming the prior distribution of homework's graded is completely unknown, the uninformative prior will be uniform. And we don't really care about which homework's in the past which were graded, just how many, let's call it $x$.

Therefore the probability of any given homework in the future from time $t = [1,15]$ being marked should all be equal, and equal to $\frac{5-x}{15-t}$

p.s. Just do all your homework, stop trying to game it.