You are given a deck of fifty two cards which have printed on them a pair of symbols: an integer between 1 and 13, followed by one of the letters “S,” “H,” “D,” or “C,” There are 4 × 13 = 52 such possible combinations, and you may assume that you have one of each type, handed to you face down.
(a) Suppose the cards are randomly distributed and you turn them over one at a time. What is the average cost (i.e. number of cards turned over) of finding the card [11,H]?
(b) Suppose you know that the first thirteen cards have one of the letters “H” or “D” on them, but otherwise all cards are randomly distributed. Now what is the average cost of finding [11,H]?