Understanding Monte Carlo Probabilities

Question

I am trying to get a good grasp on Monte Carlo (MC) algorithms, but I feel I am missing something fundamental.

What I don't understand is how MC improves its confidence of giving the correct solution by running more executions.

So please correct me if I am wrong and assume that $Pr[false] \leq 0.5$. Assume we need to find the number of executions so that $Pr[false] \leq 0.125$, thus improving confidence.

Is it true that the number of needed executions is $3$, since $0.5^3=0.125$?

Thanks in advance...