I did some research on my DS. I tested 200 moves and found 103 moves worked and 97 didn't. So the chance must be 50%.
Only traded Pokemon can rebel against a trainer. They only rebel when they are higher than the level the badges allow the user to control. For example, until beating the 4th gym leader in all the games, all traded Pokemon higher than L.30 will 'rebel'. Once you beat the 6th gym leader, you can train traded Pokemon to L.50 perfectly before they started disobeying. The last badge allows you to train traded Pokemon to L.100. If you have no badges, the highest level you can train a traded Pokemon without it disobeying is L.10. Source