Problem: You are given a fair coin, how to get an unfair coin with probability of heads = 1/3 and probability of tails is 2/3. Answer: Find the binary representation of 1/3 and 2/3 1/3 = 0.01010101... 2/3 = 0.10101010... Keep tossing a coin till you get a head. If the head fall on the even position, call it a head If the heads fall on an odd position, call it a tail. With this method you can get an unfair coin of any probability - even a probability of head = 1/Pi and the probability of tail is 1- 1/Pi (all you need to do is to get the binary exapansion of 1/Pi and 1-1/Pi)