100 students, 32 oral groups. If I write reports for half the students in the group (50), what's the probability I will end up writing a report for at least someone in each oral group?

I don’t have enough time right now to work out a solution, but here is what I quickly figured out:
There 28 groups of three students and 4 groups of four students.
Assuming the absolute worst-case scenario, you have reports from at least 16 of the 32 groups, so you are guaranteed to cut your work-load in half.

It is probably easier to run a computer simulation. This problem is complex because not every group has an equal opportunity of being chosen, and the size of the sample doesn’t match up with the number of groups.

If you choose a group of three, the probability of the group not being represented is slightly less than 1/8, but this isn’t very useful because the groups are not mathematically independent.

I think that I can have the results of a computer simulation in a few hours.

The probability is 100% if you look at the groups beforehand and decide which reports to write.

Am I missing something?

@the100thmonkey I assumed that 50 students for the full report were already chosen. Of course, if those 50 reports aren’t already written, then the OP could strategically choose the 50 people.

The 50 were randomly selected (and the reports have already been written).