FALSE.  You should switch to a different door.  By not switching, you would have a 1 in 100 chance of winning—a probability of 1%.  Consider what happens if you switch.  There is a 99 in 100 chance that your original choice was not the winning door.  Then, among the 50 remaining doors, there’s your selected door and 49 others.  To win you need to switch from your selected door to the winning door (1 in 49 chance).  So by switching doors, your probability of winning is 99/100*1/49 = 2.02%. 

You are correct!  Your probability of winning more than doubles by switching.  Not switching would give you a 1 in 100 chance of winning.   By switching, there is a 99 in 100 chance that your original door was not a winner and a 1 in 49 chance that you will move from a non-winning door to the winner, so the probability of winning is 99/100*1/49 = 2.02%