Consider a Game That Consists of Dealing Out a Hand

question 108

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) \[\begin{array} { l | l r r r }
• \mathrm { X } & 12 & 19 & 20 & 21 \\
• \hline \mathrm { P } ( \mathrm { X } = \mathrm { x } ) & 1 / 4 & 1 / 4 & 1 / 4 & 1 / 4
• \end{array}\]

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