Three-sided Coin to Generate Fair Coin Toss

[hrhgroup]

generate a coin

Dear friends
This is my question:

Pure randomness. We wish to use a three-sided coin to generate
a fair coin toss. Let the coin X have probability mass function
X =
A, pA
B, pB
C, pC,
where pA, pB, pC are unknown.

(a) How would you use two independent flips X1,X2 to generate
(if possible) a Bernoulli(12) random variable Z?

(b) What is the resulting maximum expected number of fair bits
generated?

Thanks

 

[htg]

To generate Bernoulli r.v. you have to classify your results into 2 categories.
You have to know pA, pB, pC to predict what distribution you will get.
It may be impossible to get fair bits, but using long sequences of tossing results you could approximate fair bits.