M119L09to10-page6

# M119L09to10-page6 - observed relative frequencies of red...

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(Lesson 9: Probability Basics; 4-2) 4.06 Example 4 (Roulette) 18 red slots P red ( ) = 18 38 = 9 19 47.4% ( ) 18 black slots P black ( ) = 18 38 = 9 19 47.4% ( ) 2 green slots P green ( ) = 2 38 = 1 19 5.26% ( ) 38 total The casino pays “even money” for red / black bets; in other words, every dollar bet is matched by the casino if the player wins. This is slightly unfair to the player! A fair payoff would be about \$1.11 for every dollar bet. But then, the casino wouldn’t be making a profit! According to the Law of Large Numbers (LLN), the probabilities built into the game will “crystallize” in the long run. In other words, the
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Unformatted text preview: observed relative frequencies of red, black, and green results will approach the corresponding theoretical probabilities 9 19 , 9 19 ,and 1 19 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ after many bets. In the long run, on average, the casino will make a profit of about 5.26 cents for every dollar bet by players in red / black bets. We say that the house advantage is 5.26%; see the margin essay “You Bet” on p.140 . How do you maximize your chances of winning a huge amount of money?...
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## This note was uploaded on 12/29/2011 for the course MATH 119 taught by Professor Kim during the Fall '09 term at SUNY Stony Brook.

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