Let's say I have a Monte Carlo algorithm $A$ that gives the correct answer with a probability $p$ > $1/2$. I don't have any information on if it's decisional or not.

I understand that I can make another algorithm $A'$ that runs $A$ for a number of times $k$ and returns the average (or the most repeated answer of $A$). Considering this, I need to find the value of $k$ so that the error probability is at most $\epsilon$.

What I don't fully understand is what the error probability of $A'$ would be in this case. I have done other Monte Carlo exercises where the error probability would be $(1-p)^k$ after repeating $k$ times, but those were biased in the way that you could know that if $A$ returned specifically true or false, depending on the problem, the answer would be correct. Would the error probability still be $(1-p)^k$ in this case?

I've seen in other questions that I can use the Chernoff bounds for this, but since this is an exercise for my algorithmics class in university, and I don't recall having seen the Chernoff bounds or anything similar at all, I'm somewhat reluctant to using it. Also, I don't really understand how to work from that. I would like to know if I need to use Chernoff in this case to find $k$ for the error probability to be at most $\epsilon$ or if there's another simpler way.

Thank you in advance.