Find P[X + Y = 1], P[X + Y = 2].

Let X be the difference and let Y be the sum of the number of heads obtained when Car- los and Michael each flip a fair coin twice.

(a) Describe the underlying space S of this random experiment and show the mapping from S to S _XY , the range of the pair ( X , Y ).

(b) Find the probabilities for all values of ( X , Y ).

(c) Find P[X + Y = 1], P[X + Y = 2].