This is very hard to explain.
No, faith isn't in our DNA, rather its embedded in our soul.
What many want to skip over is the fact that we are made in the image of God. That doesn't necessarily mean our bodies look like Him, rather that we have (are) a spirit just as He is. (Our spirit (soul), however, is inside a physical body). Like God, we have certain "powers", or abilities (no, we are not gods). One of these "powers" is the ability to take in information, sort it out, and then draw a conclusion. God didn't make us robots; a being that can only do what it's programmed to (follow a set of predefined instructions). He made us with the ability to choose; to decide; to reason (just like Himself).
Now, one might define 'Belief' as 'weighing data and then drawing a conclusion'. The conclusion is ours alone. We can tell others our conclusion, but we cannot make it theirs. Each person must form their own conclusion from the data they have.
In the case of your example...
You took in data (visual, oral, written or whatever). Then you ran it through your “mental sieve” (formed from things you gained from observations, teachings, interactions, (and such) from the time you were born up to that point), and formed a conclusion - a belief. Your sister did the same thing. She took in the data, ran it through her mental "sieve" (things she observed or heard, read, interactions, etc.) and formed her own conclusion. How each of you chose to act upon that conclusion sent you down your individual paths. (Some paths are similar, while others are vastly different.)