4. + -15 points My Notes o Ask Your Teacher Roulette is one of the most common g

Question

4. + -15 points My Notes o Ask Your Teacher Roulette is one of the most common games played in gambling casinos in Las Vegas and elsewhere. An American roulette wheel has slots marked with the numbers from 1 to 36 as well as 0 and 00 (the latter is called "double zero"). Half of the slots marked 1 to 36 are colored red and the other half are black. (The 0 and 00 are colored green.) With each spin of the wheel, the ball lands in one of these 38 slots. One of the many possible roulette bets is to bet on the color of the slot that the ball will land on (red or black). If a player bets on red, he wins if the outcome is one of the 18 red outcomes, and he loses if the outcome is one of the 18 black outcomes or is 0 or 00. So, when betting on red, there are 18 outcomes in which the player wins and 20 outcomes in which the player loses. Therefore, when betting on red, the probability of winning is 18/38 and the probability of losing is 20/38. When betting on red, the payout for a win is "1 to 1". This means that the player gets their original bet back PLUS and additional amount equaling their bet. In other words, they double their money. (Note: If the player loses they lose whatever amount of money they bet.) Scenario: Mike goes to the casino with $700 in his pocket and decides to place a single $150 bet on red. He knows that if he loses he will have $150 less than he started with. However, if he wins he doubles his $150, puts it in his pocket with the rest of his money, and walks away. What is the expected value for the total amount of money he will have in his pocket after he has made this bet (and either won or lost)? (Give your answer correct to the nearest cent.)

Explanation / Answer

Probability of winning = 18/38
Probability of losing = 20/38

When he wins, the total amount in his pocket will be $700 + $150 (winning amount) = $850
When he loses, the total amount in his pocket will be $700 - $150 (lost amount) = $550

Expected amount in his pocket = Probability of winning * $850 + Probability of losing * $550
= (18/38) * 850 + (20/38) * 550 = $692.11

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