What must the questioner do, and is expiation (kaffarah) obligatory upon him, due to a traffic accident he caused, injuring three workers, one of whom is paralyzed and another with severe fractures, knowing that he does not know whether he was speeding or inattentive while driving?

The driver who caused the accident due to speeding and inattentiveness is liable for what resulted from it. If the injuries amount to one-third of the blood money (Diyya), it shall be borne by his 'Aqila (male relatives on the father's side). If it is less, it shall be from his personal wealth.

As for what is paid by insurance companies that are not founded on a Sharia-compliant methodology, it is not permissible to take more than the amount paid to the company, based on the Almighty's saying: "And if you repent, you may have your principal – [thus] you do not wrong and you are not wronged."

The driver must complete the rights of the injured parties if the insurance company falls short in any of it.