I'm having a hard time understanding the way Arthur verifies proofs probabilistically with coin tosses in an intuitive manner.
Suppose Arthur is a logician equipped with paper, a pencil and an unbiased coin. Someone hands Arthur a proof that some string s is in some language L. How exactly does Arthur probabilistically check the proof? My interpretation is that he does the following:
Arthur tosses the coin. If it lands showing heads, he accepts the first statement without checking it. If it lands tails, he checks it. If, upon checking, he determines that the first statement is false, he rejects the proof. Otherwise, if he determines that the first statement is true, he continues this process with the next statement of the proof. If Arthur never rejects the proof during this process, then he accepts the proof if one of the statements is a concluding statement of the form "..., hence s is in L" and he rejects the proof otherwise.
Is this a correct interpretation?
Edit: I am not talking about probabilistically checkable proofs. The question above came about from thinking about the class MA.