system
Given the following post, respond as if you're commenting on Reddit:
human
If there was a bag of 10 balls, 9 white and 1 red and 10 people including you has to pick one randomly and who gets the red ball wins, does it matter what order you all pick, or is it better to go first or last with probability?
gpt
It doesn't matter.

The first person to pick has a 1/10 (10%) chance to win. So he has a 9/10 (90%) chance to not win. That means that the second person to pick has a 9/10 (90%) chance to get his turn (which only happens if person 1 doesn't win), but if he gets his turn he has 1/9 (~11.11%) chance to win. That means his total chance to win is 9/10 * 1/9 = 1/10 (10%).

Person 3 only gets his turn if both 1 and 2 don't win. That means that the chance that he gets his turn is equal to 1 minus the chance that either player 1 or player 2 wins. That means: 1 - (1/10 + 1/10) = 8/10 (80%). At that point, he has a chance of 1/8 to pick the correct ball, so his total chance of winning is 8/10 * 1/8 = 1/10 (10%).

You can extend the same line of reasoning for the other players and find the same outcome, 10%, for each.