The Drunkards Walk: Probability hierarchy & Monty Hall

Tl;Dr: understanding probability is hard when using vague terms. Here, have a picture

Here’s my understanding now

Imagine you want to understand the probability of something happening, assuming there are a finite number of equally probable results. For example: what are the chances of 2 dice summing to ’10’ in one throw.

The Trial is the action of throwing the dice. For now: Imagine that the dice are still in the air…

The Sample Space contains the 36 (6^2) potential configurations of how the dice will land including the sequence of each config. Each of these 36 configurations is called a sample point. The face value of the configuration of each die.

Inside the same space are two areas:

The event <- all the possible configurations that meet the result you want (dice sum to 10). If your desired outcome is ‘6’ in a single die trial, there is only 1 point that satisfies the Event criteria. For our 3 example, the Event space has 3 possible configurations (5,5; 6,4, and 4,6). The

The Compliment <- the NOT of the event: all the sample space configurations that do not meet the event criteria. For the single die example above, there are 5 points in the Compliment.

Now… Advance yourself in time half a second:  The dice land and resolve into a single configuration. This is called the Outcome. Let’s declare it to be 6,4. Because this meets the Event Criteria the trial was successful.

I don’t really like these terms, and it’s not clear if the Drunkards walk or probabilits in general uses these terms. Hrmm…