Magic Awakening

The first step of becoming a magician is the magic awakening. This is usually conducted during a magic high school’s opening ceremony, witnessed by the school’s teachers. At that moment it’s possible to awaken the magic element within a person. 
Awakening, just as the name suggest is to awaken the potential magic that lies dormant within a person. While not explicitly shown in the story, it was stated that the number of mages are very few compared to ordinary people indicates that not everyone can successfully awaken magic.
The chances for a Mage to awaken specific Element depends greatly on how pure or how much Elemental composites of the preferred Element is in the Awakening Stone. The awakening Stones with higher purity are called Guiding Stone, as the name implies the purity of the stones are high enough to 'guide' a mage to the Element of their preferred choice. Like everything else, Guiding Stones are far more expensive than Awakening Stones. The purer the Guiding Stone, the more expensive it is.
In addition, once a person breakthrough to higher stages or Tier of Magic, they will be able to awaken another Element. The Magic Association controls the awakening Stones and people have to pay a large sum of money to be allowed to use Awakening Stones. Though this process, the paying mage can opt to use different, higher quality Element orientated Awakening Stones for a greatly increased their chances of awakening the Element of their choice. 
For example, the mage who paid for using awakening stone can ask for a purer Lightning Awakening Stone to greatly increase the chance of awakening Lightning Element at Mid Tier. However, the chance will never be 100% and there will still be a relatively huge chance for the Mage to awaken a different Element. 
It explicitly stated in the novel that humans by nature have a very chaotic physique and mental status, the Awakening Stones used in Schools are the cheapest and most abundance of its kind. They are fill with too much impurities. Both factors of humanity and the awakening stone caused the awakening in School to be extremely random. The chance of a student awakening an Element also greatly depends on luck as a result, if the awakening stone used in a particular class has that little bit more lightning element in it, the students in the class will have a slightly better chance of awakening this element than say another class' awakening stone composition has a much higher Earth or other Elements in it.