RP ⊆ BPP

Inclusion · folklore

Statement

RP $\subseteq$ BPP — folklore.

Sketch

Run the $\mathbf{RP}$ machine twice on independent coins and accept if either run accepts: the acceptance probability rises from at least $1/2$ to at least $3/4\ge 2/3$ on yes-instances and stays $0$ on no-instances.