Fair toss from a Biased coin

Problem:

Given a biased coin that turns up heads 60% of the times, can we simulate an unbiased coin toss?

Solution:

The solution to this problem is attributed to Von Neuman, which makes use of symmetry.

• Toss the coin twice.
• If it comes either HH or TT, ignore and toss again.
• If it comes up HT, output a H and if comes up TH, output a T

Why does this work?

We need to come up with a way to toss the coin that has equal probability for its outcome.

P(HH) = 0.6*0.6

P(TT) = 0.4*0.4 

Since, P(HH) != P(TT), we ignore the outcome and repeat the toss again.

P(HT) = 0.6*0.4 == P(TH) = 0.6*0.4

Now that the outcomes have same probability, biased is removed!