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?


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.

The probability of your friend guessing a number is not 1/20, the probability is 1. Unless there is a chance he would fail to guess anything or a chance he would guess something not on the D20.
So the formula for your friend guessing the correct outcome of the roll is:
1 * 1/20
or 1/20
Now, the odds of you guessing what your friend is going to guess and then that guess being correct, that would be 1/400. But that doesn't appear to be the situation.
