Probability Simulation

You have a fair coin. You want to simulate a biased "coin" that comes up heads with probability $p$ for any $p\in [0,1]$ whose binary expansion you can produce.

A.

For $p=1/3$, describe an algorithm using only fair coin flips.

B.

Generalise: given any $p\in [0,1]$, give a procedure that outputs "heads" with probability $p$ and "tails" with probability $1-p$, using a finite expected number of fair coin flips.