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).
A){12,19,20,21},equally likely
B){12,19,20,21,22},not equally likely
C){12,19,20,21,22},equally likely
D){12,19,20,21},not equally likely
E)19,20,21,22},not equally likely

Question

Quizplus · Accepted Answer

The possible combinations of two cards and their total counts are: AsAh (12), AsKs or As9h (either 11+10 or 11+9, so 21), AhKs or Ah9h (also 21), and Ks9h (19). There are no combinations that would result in a total count of 22 because the maximum value for an Ace is considered 11, and the other cards do not combine to exceed 21. The combinations are not equally likely because there are more ways to achieve a total count of 21 (four ways: AsKs, As9h, AhKs, Ah9h) compared to the other totals (one way each for 12 and 19).

Consider a Game That Consists of Dealing Out a Hand