Book of Acts
"And they said, Believe on the Lord Jesus Christ, and you shall be saved, and your house."
This verse in isolation appears to teach group salvation based upon an individual person in the family having faith. And as beautiful as scripture like John 3:16 and the like are, this above verse is why we don't isolate verses and make them dance to our tune. Verses aren't meant to be read as standalone doctrines, they're numbered and divided like that for ease of reference.
So in context this verse is an answer to a prison warden tasked with guarding Paul and Silas, who at this point were singing praises to God from their prison cells. There's an incredible earthquake (v. 26), and this man who's called “the keeper of the prison” awakes from his sleep and sees that the cell doors are all sprung open. Upon seeing this he grabs his sword and plans to take his own life, still Paul shouts from inside the darkness of his prison cell to reassure the man that he's still confined. He had an opportunity to escape but didn't take it, it's just another incredible display of God's power on Paul's behalf.
Paul and Silas had already been whipped, beaten and locked away so I'm not sure how much power they'd have to race out the front door. Still the text also says the prisoner's "bands" were loosed, which is another word for chains or shackles. So not only are all of the doors swinging open, which an earthquake could cause to happen, but the chains are off too (which I can't picture an earthquake doing). Now the jail keeper is suitably impressed by these men, so much so that he asks them this question in verse 30. He asks how am I to be saved.
That's a funny question because just a minute ago this man is ready to end his life for fear of the torturers, and that's because any man who allowed a state sponsored prisoner to escape was in danger of being killed himself. One minute he's so frightened that he's ready to end it all, but seeing that these men are righteous and kind, so kind as to stay in prison to keep him alive, he asks right away what should I do. The text says he asks for a torch to see and is trembling as he enters into the cells.
So here we're reading about a lone man afraid for his life, not so much concerned with the lives of his family. Paul's answer is to say you're saved by believing, you and your entire household are saved in the same way.