The order doesn't matter dricc, from what I understood of the game. SO it is 1 / 120, rather than 1 / 720 - still a very low chance.
But a 50% chance is silly, given the nature of the game. The only way to do so fairly would be to reduce the number of balls to 2 and have the user just choose 1. Otherwise, you'd need to invent an algorithm where the actual spot chosen doesn't matter, but it just calculates a fairly high chance you get one of the numbers chosen. But then the game just seems ridiculous.
If you want a game with a 50% chance to win, then just randomize a variable and do it with events. The purpose of having a game like this would be lost if you did it with 50% chance.