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?

What is the chance a D20 lands on 20? 5%.
What is the chance a D20 lands on 7? 5%.
What is the chance a D20 lands on [whatever number your friend named]? 5%.
No matter how you select a specific number from 1-20, a D20 has a 5% chance of matching it. Any particular number is always 5% likely, regardless of whether your friend chooses that number or not.
