***Households believed in Christ.***
It never says that.
"It never says that."
***
Without faith it is impossible to please God. If the households remained unbelieving, then baptizing them only converted them from DRY sinners into WET sinners. The Ethiopian asked Philip the evangelist in the Book of Acts: "Here is a body of water. What prevents me from being baptized?" Philip answered: "If you believe in your heart, then you may".
The EXERCISE OF FAITH is the prerequisite to water baptism.