3 / 26 Classical & Conditional Probability

Biased Coins

Assume you have a biased coin where the probability of getting heads is 2/3 and tails is 1/3. Is there a method that could be used to obtain an even (50-50) chance outcome using this coin? If so, how would you achieve it?

A

Yes. Flip three times and use the majority result without discarding anything.

B

Yes. Flip twice, map HH to one outcome and HT or TH to the other, and discard TT.

C

Yes. Treat heads as one outcome and tails as the other on a single flip.

D

No. A biased coin cannot be transformed into an exactly fair outcome.