Is there a 1 in 20 or 1 in 400 chance of guessing the outcome of a d20 roll before it happens? My friends are in a bit of an argument over Dungeons & Dragons.
My player managed to guess the outcome of a D20 roll before it happened, and my friend said that his chance of guessing the number was 1 in 20. Another friend argues that his chance of guessing the roll is 1 in 400 because the probability of him randomly guessing a number and then rolling it were both 1 in 20 so the compound probability is 1 in 400. Which of these probabilities is a better characterization of our situation, and what were really his chances?

Your another friend is arguing that:

*

*Guessing the roll; and

*Rolling the roll.

Are independent events. But that's not what you are measuring. You a measuring:

*

*Only the matching (of guest and roll has the same value).

There is one guest and 20 possible roll outcomes. So a chance of 1/20.
