I have a coin that is biased: I know that tails come up with a probability of 55%, rather than 50% as is the case with a fair coin. I would like to make a fair random choice between 2 options A and B. I want to make the random decision fair by using a combination of several flips instead of one.

What is the minimum possible number of times I need to flip the coin (if I am lucky)?

The problem is inspired from the original question in the Plus Magazine.