You know, I've never really given this particular account much reflection...what a beautiful story, and a beautiful physical example of a spiritual truth. This woman, whom in Lukes account we find spent all her living trying in vain to be healed by physicians, still had enough faith to come up to Jesus and reach for his garment through the crowd, believing that he had power to heal her. It turns my mind to the fact that the Bible tells us just to believe...BELIEVE--and be saved. It's so easy! We don't have to work all of our lives and hope against hope that God will save us if we're good enough. He saves us in spite of the fact that we're not good enough, and then just tells us to believe.
As to the faith, I think it's both. Here's why: in Romans 1:17, it says "For therein [in the gospel of Christ from the previous verse] is the righteousness of God revealed from faith to faith: as it is written, The just shall live by faith." There are two faiths: our faith, and Christ's faith.
Consider: Luke 17:6 says, "And the Lord said, If ye had faith as a grain of mustard seed, ye might say unto this sycamine tree, Be thou plucked up by the root, and be thou planted in the sea; and it should obey you. As a grain of mustard seed! That's not a lot of faith...and I can't do that, in fact, I don't know anyone who can. Does that mean that we don't have a lot of faith? If so, what about Acts 8:37, when Philip says to believe with all thine heart?
The fact is (I think), that even when we believe with all of our heart...we still don't have a lot of faith. But we don't need a LOT of faith, we just need to take all that we have and place it in Jesus Christ, because where our faith ends: his begins. Romans 3:21-22 says, "Even the righteousness of God which is by faith OF Jesus Christ unto all and upon all them that believe: for there is no difference." Notice, it doesn't say faith IN Jesus Christ. This can be further seen in Galatians 2:16 "Knowing that a man is not justified by the works of the law, but by the faith OF Jesus Christ, even we have believed IN Jesus Christ, that we might be justified by the faith OF Christ, and not by the works of the law: for by the works of the law shall no flesh be justified." See, Jesus had limitless faith in the power of God: of course, he was God. The one perhaps in scripture who came closest (although still not very close) was Peter, who had faith enough in Christ to step out onto the water--and even he looked around and started to sink. But once we place all of the little bit of faith that we have inside of us, and place it in Jesus Christ, from then on we stand on his faith. He had faith enough to live a sinless life, fulfilling the law, and then to die at the end of it believing that God would raise him from the dead. So all we're left to believe is that he did it for us.
I hope this make sense...it's really quite beyond my understanding how God graciously imputes his righteousness to us through faith. But I believe it because he said he did, even though I don't quite understand it, and praise the Lord! God loved us enough to send a Savior!
God bless!