Annie and Bert play the following game. They first shuffle a deck of 52 cards. Annie flips the cards one by one until she finds a red ace. After that Bert takes the remaining deck and flips the cards one by one until he finds the other red ace. Annie wins if she flipped fewer cards than Bert, Bert wins if he flipped fewer cards than Annie. It is a tie if they needed the same number of cards. A) Denote by X, the number of cards Annie flipped, by X2 the number of cards Bert flipped and set X3 = 53 - Xi - X2. Show that (X1, X2, X3) is exchangeable.
B) Who has the higher probability of winning in this game?