Problem 22. (3.0 %) Suppose you play a matching coin game with your friendas follows. Both you and your friend have a coin. Each time, you two reveal aside (i.e. H or T) of your coin to each other simultaneously. If the sides match,you WIN a 1 from your friend if sides do not match then you lose a 1 yourfriend. You decide to go with the following strategy. Every time, you will tossyour unbiased coin independently of everything else, and you will reveal itsoutcome to your friend (your friend does not know the outcome of your randomtoss until you reveal it). Then,
(A) On average, you will lose money to your smart friend
(B) On average, you will lose neither lose nor win. That is, your averagegain/loss is 0.
(C) On average, you will make money from your friend