then it returns YES with probability at least 1/2 (otherwise, it returns NO).

In other words, the algorithm is allowed to flip a truly random coin while it is running. The only case in which the algorithm can return YES is if the actual answer is YES; therefore if the algorithm terminates and produces YES, then the correct answer is definitely YES; however, the algorithm can terminate with NO regardless of the actual answer. That is, if the algorithm returns NO, it might be wrong.

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