You got it, but I don't think what you have is easy believism. There is life-change, heart-change, conviction. Easy believism is (I think) walking an aisle, saying a prayer, and going out for a cup of coffee. In other words, there's nothing there. I could be wrong, though.
If someone tells me they sincerely prayed and asked Jesus to save them, I tend to believe them. All I can go by is what a person confesses.
Folks in the Bible knew when they believed. Take the Ethiopian eunuch;
Acts 8:34 And the eunuch answered Philip, and said, I pray thee, of whom speaketh the prophet this? of himself, or of some other man?
35 Then Philip opened his mouth, and began at the same scripture, and preached unto him Jesus.
36 And as they went on their way, they came unto a certain water: and the eunuch said, See, here is water; what doth hinder me to be baptized?
37 And Philip said, If thou believest with all thine heart, thou mayest. And he answered and said, I believe that Jesus Christ is the Son of God.
38 And he commanded the chariot to stand still: and they went down both into the water, both Philip and the eunuch; and he baptized him.
39 And when they were come up out of the water, the Spirit of the Lord caught away Philip, that the eunuch saw him no more: and he went on his way rejoicing.
People in the Bible did not "wonder" if they believed, they knew they believed on Jesus. You don't see any promise here to turn from sin and lead a holy life, this Ethiopian eunuch believed the OT scriptures that Jesus had died on the cross for his sins and rose from the dead.
Another example is Acts 19;
Acts 19:2 He said unto them, Have ye received the Holy Ghost
since ye believed? And they said unto him, We have not so much as heard whether there be any Holy Ghost.
3 And he said unto them, Unto what then were ye baptized? And they said, Unto John's baptism.
4 Then said Paul, John verily baptized with the baptism of repentance, saying unto the people, that they should believe on him which should come after him, that is, on Christ Jesus.
5 When they heard this, they were baptized in the name of the Lord Jesus.
6 And when Paul had laid his hands upon them, the Holy Ghost came on them; and they spake with tongues, and prophesied.
Again, people in the scriptures did not wonder if they believed on Jesus, they knew. And again, do you see these disciples promising to stop sinning and turn over a new leaf? No, they believed Paul's message that John the Baptist was preaching Jesus to them and they believed on Jesus and were baptized.
Examples in the scriptures seem pretty easy to me.