Three people \(A, B,\) and \(C\) are sitting on stairs one after another such that \(C\) on the first stair cannot see the two above him and \(B\) on the second stair cannot see the one above him. There are 2 red and 2 white hats available and each person is wearing one of them. However, no one knows the color of their hat.

The following conversation then took place between \(A\) and \(B\):

\(A:\) I don't know which color hat I'm wearing.

\(B:\) At first I didn't know, but I know the color of my hat now.

If \(C\) is wearing a red colored hat, what color hat is \(B\) wearing?

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