In Acts 16 we read of Paul telling the jailer to “believe in the Lord Jesus and you will be saved — you and your household.” The jailer listens, acts on what he hears (by washing all their wounds and setting a meal before them), and his whole house is saved. However, we don’t read of other members of his household giving their testimony, their story of being swept away in God’s grace, and understanding their need of Him for salvation. I know God is the same always. I know He isn’t going to change his method of salvation. But I find it difficult to defend passages that seem to contradict one another.
From John 3:16, John 6:28-29, John 6:40, Ephes. 1:13-14 and others it’s clear that our salvation is based on our personal belief in the Lord’s death on our behalf, as confirmed by His resurrection. Matt. 7:7-8 and Romans 10:9, 13 further state that we all have to ask for ourselves in order to receive it. If Acts 16:31 means that only the jailer had to believe to save his entire household, it would be contradicting one of the basic tenants of our salvation. Therefore even though it’s not described in the passage, the fact is that every member of the household had to believe and ask to be saved in order for them all to be saved.
It’s important to remember that when various passages seem to contradict one another, the problem is always – always – a matter of our understanding. The Bible, being the Word of God, cannot contradict itself.