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 probability model for X.

A) $$\begin{array} { l | l c r r } \mathrm { X } & 1 & 9 & 10 & 11 \\\hline \mathrm { P } ( \mathrm { X } = \mathrm { x } ) & 1 / 4 & 1 / 4 & 1 / 4 & 1 / 4\end{array}$$
B) $$\begin{array} { l | l r r r } \mathrm { X } & 12 & 19 & 20 & 21 \\\hline \mathrm { P } ( \mathrm { X } = \mathrm { x } ) & 1 / 6 & 1 / 6 & 1 / 3 & 1 / 3\end{array}$$
C) $$\begin{array} { l | l r r r r } \mathrm { X } & 12 & 19 & 20 & 21 & 22 \\\hline \mathrm { P } ( \mathrm { X } = \mathrm { x } ) & 1 / 5 & 1 / 5 & 1 / 5 & 1 / 5 & 1 / 5\end{array}$$
D) $$\begin{array} { l | l r r r r } \mathrm { X } & 2 & 12 & 19 & 20 & 21 \\\hline \mathrm { P } ( \mathrm { X } = \mathrm { x } ) & 1 / 12 & 1 / 12 & 1 / 6 & 1 / 3 & 1 / 3\end{array}$$
E) $$\begin{array} { l | l r r r } \mathrm { X } & 12 & 19 & 20 & 21 \\\hline \mathrm { P } ( \mathrm { X } = \mathrm { x } ) & 1 / 4 & 1 / 4 & 1 / 4 & 1 / 4\end{array}$$