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 friend is confusing the situation where both players roll the same specific number (which would give you 1/400) vs the situation you are in where they have to roll the same number but it could be any number (1/20). I suppose your confusion is that you have to roll the specific number your friend guessed but, which makes it seem like the first situation I described, however the difference is that your guess could have been any number.
