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Home > CCG > Chapter 11 > Lesson 11.2.1 > Problem 11-87


In the card game called “Twenty-One,” two cards are dealt from a randomly shuffled deck of playing cards. The player’s goal is to get the sum of his or her cards to be as close (or equal) to as possible, without going over . To establish the sample space for this problem, you need to think of choosing two from a set of .  


  1. How many ways are there to be dealt two cards?

  1. The tens, jacks, queens, and kings all have a value of points. There are four of each in a standard deck. What is the probability of being dealt two ten-valued cards?

    How many ways are there to select two cards from the set of ten-valued cards?

    Divide this number by the total number of -card hands.

  2. If you did not already do so, write your solution to part (b) in the form .

  3. What is the probability (as a percent) of being dealt two face cards? (Face cards are Kings, Queens, and Jacks, that is, the cards that have faces.) Also write your answer as .

    See part (b).

  4. In “Twenty-One” an Ace can count as point or points. The deal is called “soft” when the Ace is counted as points. What is the probability of being dealt a “soft ,” that is, a card worth ten points and an Ace?

    See part (c).