“And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house.”
King James Version (KJV)
16:31 Thou shalt be saved and thy household - If ye believe. They did so, and were saved.
Ac 16:31 Believe on the Lord Jesus Christ. He was a heathen. Faith was the essential step. To Jews, on the day of Pentecost, already believing Peter's proposition, he said, in answer to the same question, "Repent and be baptized" (Ac 2:38); but the heathen jailer was not ready for this. Faith must first be wrought, and then that faith, leading to the acceptance of Christ, would save. His faith would save, because it would be the power that would lead him to follow Christ. And thy house. We learn from the next verse that "all that were in his house" could listen the "word of the Lord" (Ac 16:32), hence were not infants.