Is it known that "For each problem in NP there is a randomized algorithm that solves it in polynomial time"? If not true then is there any proof of that. Or does it belongs to the unknown domain?

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# Is there any proof that says "For each problem in NP there is a randomized algorithm that solves that problem in expected polynomial time."

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Is it known that "For each problem in NP there is a randomized algorithm that solves it in polynomial time"? If not true then is there any proof of that. Or does it belongs to the unknown domain?

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