Cryptography

A) You have a set {a, b, c, d} of four elements and you need to choose one of these elements uniformly at random. That is, each element has equal probability 1/4 to be chosen. You have a coin that comes up heads with probability 1/3. How can you use this coin to make the choice? Describe a method where the expected number of tosses is less than 5 What is the expected number of tosses in your method?

B) This question is about the method that you described in the previous exercise (A). Does there exists a method with a smaller expected number of tosses? If so, what is this method and what is its expected number of tosses?