How do EMTs know who to take care of first?

Generally the most quite patients are the most serious ones. For example if u walk into a room with two patients, one on the floor not moving and eyes closed and the other walking around with a small cut on his arm, the one on the ground is the most serious one.

The reason is because is that there is a possibility that the quite person is not breathing and/or has no pulse. The longer they are there in the condition, the lower the chances of his/her survival.