A paradox is any statement that appears to contradict itself. That includes both actual contradictions such as Russel's paradox and statements that appear to be

A paradox is any statement that appears to contradict itself. That includes both actual contradictions such as Russel's paradox and statements that appear to be invalid, but have non-obvious valid conclusions like the Monty Hall problem. This problems falls into the second category. We are given what appears to be a well-defined problem, but when we solve it in different ways, we get different answers. The resolution to the paradox is the problem isn't well defined because your technique for generating randomness will produce different answers.