Ok, so I have a problem that is equivalent to this game:
Two players each choose $k$ random integers between 1 and $n$ independently of each other. What is the probability that they both choose the same numbers?
Now I have a table of measured data for the probability of each number, but there are two catches.
The numbers are chosen at uneven distributions
The data I'm given is the percent of games each number appears in. Since up to 10 numbers can be selected each game, the total percent is greater than 100.
I have no idea where to go from here or how to work with this.
Example of data: percent of games each number was chosen 1-10% 2-5% 3-6% ...