Originally Posted by

**Gekko** We choose two groups where group A can be of size X where X ranges from 1 to n-1. Group B is the remaining (n-X).

All values of X are equally likely and all group sizes are equally likely

If we choose one item from 1 to n where all choices are equally likely, what is the average size of the group containing the item?

3. The attempt at a solution

Originally I tried the following:

Average size of group A is simply n/2 as it is uniformly distributed and therefore, since the item can be in either group, the size must also be n/2

However, given that the item is more likely to be in the larger of the two groups, we must skew the average to greater than n/2 and indeed, when I run an Excel simulation, that proves correct. Any thoughts on this?