Is salvation primarily based upon luck?

[Boris]

This could apply to the doctrines of Christianity or really any exclusive religion.

Assume that the following are necessary for salvation:

1. Belief in a certain God (such as Jesus Christ)
2. Good works (i.e. engaging in morally correct behavior as defined by religious texts such as the bible)

The first tenet is what perplexes me. Said belief in a particular God is primarily based upon where one is born and geographically resides as well as the nature of one's family members. Since one does not control those factors, it's nothing short of luck as to whether or not the first tenet is satisfied. Assuming Christianity is the "correct" path to God, someone such as me, born into a non-Christian family, has been blessed with luck that virtually everyone around me is a Christian and therefore have been influenced by its beliefs. Had I been residing in India instead of the United States, I wouldn't have had that opportunity.

Basing salvation on factors that one cannot directly control seems rather irrational for a being that is allegedly all-knowing. So therefore, I draw into question that veracity of tenets necessary for salvation. Although I'm sure they're probably leaps and bounds in my logic so someone please tell me I'm a moron.

[Boris]

The Catholic Church believes that anyone can be "saved," but in order to do so they must accept Christ.  For those who died following other faiths, this happens at an unspecified time following their death when Christ presents himself to the deceased in all his glory.

So then what rational basis is there for adhering to Catholic doctrines throughout one's lifetime? With nothing tangible to prove or disprove the validity of Catholic thought, one might as well wait until they have died to learn the truth. What benefits other than possible intrinsic satisfaction (which is most likely entirely dependent upon the person rather than the religion itself) come from being a Catholic?

Or am I looking at it the wrong way?