Suppose that you and a friend are playing cards and decide to make a bet. If you draw two non-face cards, where a face card is a Jack, a Queen, or a King, in succession from a standard deck of 5252 cards without replacing the first card, you win $10$⁢10. Otherwise, you pay your friend $20$⁢20. What is the expected value of your bet? Round your answer to the nearest cent, if necessary.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Suppose that you and a friend are playing cards and decide to make a bet. If you draw two non-face cards, where a face card is a Jack, a Queen, or a King, in succession from a standard deck of 5252 cards without replacing the first card, you win $10$⁢10. Otherwise, you pay your friend $20$⁢20. What is the expected value of your bet? Round your answer to the nearest cent, if necessary.

Expert Solution
Step 1

Given information:

The number of cards in a deck is 52.

The set of 52 cards are divided into 4 suits. The 4 suits are:

  • Diamonds
  • Clubs
  • Hearts
  • Spades

Now each of the 4 suits are divided as given below:

(Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King).

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