for my Data class project we had to play a board game and do an analysis of it. My group chose rehashed version of Snakes and Ladders. I am almost done the majority of the project, but am stuck on creating the sample space, this is what I have to accomplish:
describe a sample space as a set that contains all possible outcomes of an experiment, and distinguish between a discrete sample space as one whose outcomes can be counted (e.g., all possible outcomes of drawing a card or tossing a coin) and a continuous sample space as one whose outcomes can be measured (e.g., all possible outcomes of the time it takes to complete a task or the maximum distance a ball can be thrown)
This is the board we used.
https://erdenetefl.files.wordpress.com/2011/03/game-board.jpg
There were 3 players and we played 3 games. I don't exactly understand how to make the sample space for this game. This is a do it yourself unit in our school. I am not asking for answers but it would be helpful if you can give me a lead.
The sample space should, typically, contain all possible outcomes of an experiment. Presumably, the experiment here is playing a single game. So, the sample space should be a description of a game that contains all the information you find interesting. For example, if all you care about is the length of a game, then your sample space could be all natural numbers (for the number of turns it took). If you care about the specific way the game went, it might be a full description of each position of each player at each turn. Or it might even include the particular throws each player made. And so on.
Here is a very simple analogous example. Suppose you have silly game that goes as follows: you throw a single die once. If it comes up 6, you win. If it comes up 1-5, you lose.
The obvious sample space here should be $$ \{1,2,3,4,5,6\}, $$ as these are the outcomes of the experiment. However, you could also say that the sample space should be $$ \{\text{win, lose}\}, $$ if you only care about the fact that the player could either win or lose, and not care what the die throw was in case of a loss. Which one of these you choose depends on which information you find relevant.