You and two friends decide to go to a casino and play Blackjack. You find an empty table and sit down. The dealer shuffles and deals from a new 52 card deck. In order to win, you and your friends know that you need to either score a 21 (blackjack and automatic win) or get a higher total than the dealer. You know that a deck of cards has 13 different cards (2-10, Jack, Queen, King, and Ace), and that there are 4 copies of each in the deck. You know that an ace is equal to either 1 or 11 and that Jacks, Queens, and Kings are worth 10. The dealer deals out the following cards: You: Jack and Ace Friend 1: King and 10 Friend 2: 10 and 10 Dealer: 10 and ? The dealer is about to deal their last card. What are the following probabilities: A) What is the probability that the next card can beat your hand?   B) What is the probability that the next card can tie your hand?   C) What is the probability that the next card can beat your friends?

Q: Would you play the game? Why or why not?

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Q: How many outcomes are possible?

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Q: Is the game fair? How many dollars should Jane pay for a draw in a fair game?

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Q: how many pairs (two cards with the same face and three cards with all different faces) are possible…

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.