I have no formal background in math, statistics, or anything. Just trying to figure out a fun problem with a game of dice.
Lets say you have 3 people sitting a table rolling dice (including yourself).
This is what the result set looks like:
You: [5, 4, 3, 2, 1] P1: [x, x, x, x] P2: [x, x, x, x, x]
So you know what dice you have but not what the others have. Now P1 guesses that there are 3 fives on the table. What is the probability that there are actually 3 fives on the table?
Since there are 9 unknown dice, I know there are 531,441 possibilities that could have been rolled (9**6). But past that I'm not sure what to calculate next.
EDIT: After thinking about it, 9**6 is probably invalid because although someone could get [5, 4, 3, 2, 1] and [1, 2, 3, 4, 5] that is the same thing for what I'm trying to do, which is find out how probable it is to have X amount of a specific face value (i.e 4 fours)