# Showing that $BPP \subseteq EXP$?

I am trying to understand why $$BPP \subseteq EXP$$. This question almost gives the answer (simulate $$BPP$$ machine on all possible toin cosses and then "act accordingly"). However, it is not clear to me what act accordingly means: I am thinking we need to count how many times the probabilistic Turing machine accepts and how many times it rejects and then act upon this information - but how exactly?

A $$\mathsf{BPP}$$ machine $$A$$ has randomness complexity $$r(n)$$ which is polynomial in $$n$$. Hence, an $$\mathsf{EXP}$$ machine $$B$$ can loop over all $$2^{r(n)}$$ values of the random tape of $$A$$, simulating $$A$$ with each random input (each simulation taking polynomial time), and count how many times $$A$$ accepts or rejects. The overall decision of $$A$$, then, is whichever of the two counters contains a larger value at the end of this process.
Interestingly, the same reasoning also explains why $$\mathsf{PP}$$ is contained in $$\mathsf{EXP}$$.