Consider a Game That Consists of Dealing Out a Hand

Multiple Choice

Consider a game that consists of dealing out a hand of two random cards from a deck of four cards.The deck contains the Ace of Spades (As) ,the Ace of Hearts (Ah) ,the King of Spades (Ks) and the 9 of Hearts (9h) .Aces count as 1 or 11.Kings count as 10.You are interested in the total count of the two cards,with a maximum count of 21 (that is,AsAh = 12) .Let X be the sum of the two cards.Find the expected value of X.

A) 19.0
B) 18.0
C) 20.5
D) 18.5
E) 20.0