The Dungeons and Dragons problem
Last week I posed this problem in my Bayesian Statistics class:
Suppose there are 10 people in my Dungeons and Dragons club; on any game day, each of them has a 70% chance of showing up.
Each player has one character and each character has 6 attributes, each of which is generated by rolling and adding up 3 6-sided dice.
At the beginning of the game, I ask whose character has the lowest attribute. The wizard says, “My constitution is 5; does anyone have a lower attribute?”, and no one does.
The warrior says “My strength is 16; does anyone have a higher attribute?”, and no one does.
How many characters are in the party?
My solution is in this Jupyter notebook: