The unconverted would go to the Lake of Fire not because God did not elect them, but because of their willful rebellion before God. However, the believer will go to Heaven not because the person chose God but because God has chosen the person for salvation. Salvation is of the Lord. If you are saved it is only because God the Father has chosen you before the foundation of the world (Ephesians 1); the Lord Jesus Christ took you place under the wrath of the Father (2 Corinthians 5:21) thus paying your penalty in full; and the Holy Spirit, in the appointed time of God, has regenerated you–giving your spiritual deadness new life that you can now see your need of salvation and you come to God in repentance of your sin and faith in the Lord Jesus Christ alone as your one and only way of salvation. Sola Gratia.