(a) Consider the set n] 2]. We can generate a subset X of this set as follows: a fair coin is flipped independently for each element of the set [n]; if the coin is head, then the element is included in the set X, and otherwise it is not. Argue that the resulting set X is equally likely to be any one of the 27 possible subset:s. This gives you a simple way to generate a uniformly random subset of In]. (b) Suppose that two sets X and Y are chosen independently and uniformly at random from all the 2" subsets of [n]. Calculate the following probabili- ties: P(X-Y), and P(X UY _ [n]) Hint: (1) You can use the procedure (a) to calculate the probabilities. (2) The answers are simple. (a) Consider the set n] 2]. We can generate a subset X of this set as follows: a fair coin is flipped independently for each element of the set [n]; if the coin is head, then the element is included in the set X, and otherwise it is not. Argue that the resulting set X is equally likely to be any one of the 27 possible subset:s. This gives you a simple way to generate a uniformly random subset of In]. (b) Suppose that two sets X and Y are chosen independently and uniformly at random from all the 2" subsets of [n]. Calculate the following probabili- ties: P(X-Y), and P(X UY _ [n]) Hint: (1) You can use the procedure (a) to calculate the probabilities. (2) The answers are simple