math-probability

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A King sends for 3 prisoners. HE has 3 black hats and 2 white hats. He blindfolds the prisoners & puts a hat on each. He then removes the blindfolds & allows them to look at each other. He tells them that if they can tell him the color of the hat they have on, he will set them free. If not, they will be killed. The 1st prisoner looks at the other 2 and says, "I don't know. I can not tell." The 2nd prisoner looks at the 1st & 3rd prisoner & says, "I don't know. I can not tell." The 3rd prisoner is blind, but says, "I have a black hat on." The blind prisoner is right!
Was the blind prisoner lucky, or did he really know what he was talking about?
-thanks for the helP!!

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