Marbles

You were captured By an indian tribe, they bring you to the chief who decides to give you a chance to live. In front of the tribe he places a white marble and a black marble into a bag. He tells you in the morning, in front of the tribe, to reach into the bag, pull out 1 marble and if its white, I'll set you free. During the night the chief removes the white from the bag and replaces it with another black marble. The chief's daughter saw what her father did...comes to you, and tells you what he did. In the morning in front of the tribe, you reach into the bag, pull out one marble and they set you free. Why did they set you free?