[Mixingl: Suppose Bitcoin was changed such that transactions can have at most two inputs and two outputs (this is the case in Zerocash, for example). Alice, Bob, and Carol each have a single UTXO worth 1 BTC. They want to mix their coins among the three of them (without a trusted server) so that three output UTXOs are worth 1 BTC each and they are perfectly shuffled: All six (3!) permutations are equally likely. They decide to do the following: Alice and Bob 3. post a transaction with their two bitcoins as input and two fresh addresses, X and Y, as outputs, each holding 1 BTC. Alice controls one address and Bob controls the other, but an observer cannot tell which is which. Suppose X is listed as the first output in this transaction. Next, Carol and the owner of X post a similar transaction: Carol's coin and the coin X are the inputs, and two fresh addresses W and Z are the outputs, each holding 1 BTC. Carol controls one address and the owner of X controls the other. As before, an observer cannot tell which is which. They use Y,Z,W as the final shuffled coins. Pictorially, the mixing process looks as follows: 3 What are the anonymity sets for the addresses Y, Z, and W? Assuming that each mix independently assigns equal probability to both outcomes, what is the probability that Alice contr What is the probability that Carol controls W? a. b