As always with scripture context is everything, so let’s have a look.
*** To the married I give charge, not I but the Lord, that the wife should not separate from her husband
 (but if she does, let her remain single or else be reconciled to her husband) – and that the husband should not divorce his wife.
 To the rest I say, not the Lord, that if any brother has a wife who is an unbeliever, and she consents to live with him, he should not divorce her.
 If any woman has a husband who is an unbeliever, and he consents to live with her, she should not divorce him.
 For the unbelieving husband is consecrated through his wife, and the unbelieving wife is consecrated through her husband. Otherwise, your children would be unclean, but as it is they are holy.
 But if the unbelieving partner desires to separate, let it be so; in such a case the brother or sister is not bound. For God has called us to peace.
 Wife, how do you know whether you will save your husband? Husband, how do you know whether you will save your wife?
 Only, let every one lead the life which the Lord has assigned to him, and in which God has called him. This is my rule in all the churches.
 Was any one at the time of his call already circumcised? Let him not seek to remove the marks of circumcision. Was any one at the time of his call uncircumcised? Let him not seek circumcision.
 For neither circumcision counts for anything nor uncircumcision, but keeping the commandments of God.
 Every one should remain in the state in which he was called.
 Were you a slave when called? Never mind. But if you can gain your freedom, avail yourself of the opportunity.
 For he who was called in the Lord as a slave is a freedman of the Lord. Likewise he who was free when called is a slave of Christ.
 You were bought with a price; do not become slaves of men.
 So, brethren, in whatever state each was called, there let him remain with God.
***[FONT=Georgia]So the answer to your question is right there in verse 16.
*** Wife, how do you know whether you will save your husband? Husband, how do you know whether you will save your wife?
***[FONT=Georgia]From context then we see that St. Paul is not suggesting salvation just by being married to a believer, but the consecration of the children of such a union, and that in a Jewish context of unclean vs clean.