Is high speed rail beneficial to the environment?

One of the top benefits of high speed rail is the environment. However, if the rails are electrified, wouldn't the electricity end up be being made by a fossil fuel plant. Also, if the efficiency of a electrified train is 30% and the Efficiency of a fossil fuel plant is about 40%, that means electrified trains have an efficiency rate of 12%. Now, you can compare that to the average car, which has a 30% efficiency rate and the car is far superior. Do you agree with my math or am I wrong?