Assume I am in a draw for a prize. There are 3 rubber balls, 2 red ones (loser) and 1 green ball (winner). If the green ball is drawn, I win.
Now let's have a second draw (simultenously). It has 20 red balls and 10 green ones – same thing, 1 draw, if I get a green ball, I win.
Assume equal random distribution of the balls. Is there any difference in the win probabilities between the two scenarios?
Side note: In an uneven fight, 2 v 1 vs 20 v 10, I believe the 1 fighter vs 2 has a better probability of winning than 10 over 20 (it's easier to overcome a 2:1 advantage once than it is 20 times). Not sure if it plays into this at all :).