5. In the board game Monopoly, you roll two dice on your turn. If you roll...
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5. In the board game Monopoly, you roll two dice on your turn. If you roll doubles, you get another turn. If you roll doubles again, you get a third turn. If you roll doubles on your third turn, you "go to jail" and have to move your game piece to the "jail" space. What are the chances of going to jail on your turn? (Ignore the other ways you might go to jail.) 6. If you roll two dice, the probability that one of the dice is a 3 and the other is not a 3 is: X+ Explain the calculation with words. 7. + In Yahtzee, you roll five dice at the same time. If all five dice display the same number, you get to yell "Yahtzee!" and get 50 points. What are the chances you get to yell "Yahtzee!" after a roll? 8. You roll three dice and want to get a 6 on at least one of them. (a) Are the chances of this happening more than, less than, or equal to ½? (b) Are the chances of this happening more than, less than, or equal to:+1+ ? 6 6 6 9. (The Paradox of the Chevalier de Méré). In a gambling game, players bet on the event that in 4 rolls of a die, a 1 (called an "ace" here) would occur at least once. In another game, players bet on the event that in 24 rolls of a pair of dice, a double ace (that is, a 1 on both dice at the same time) would occur at least once. A French nobleman, the Chevalier de Méré, believed that both events had the same chances. He reasoned: 63 *If I have a chance of getting an ace on one roll, then in 4 rolls I have a 4xchance of getting an ace at least once. *If I have a chance of getting a double ace on one roll of a pair of dice, then in 24 rolls I have 36 a 24×chance of getting a double ace at least once. 36 3 However, the gamblers found that the first event was a bit more likely than the second. What is wrong with the Chevalier's reasoning? 10. If you roll three dice, what are the chances exactly one of them will be a 6? 5. In the board game Monopoly, you roll two dice on your turn. If you roll doubles, you get another turn. If you roll doubles again, you get a third turn. If you roll doubles on your third turn, you "go to jail" and have to move your game piece to the "jail" space. What are the chances of going to jail on your turn? (Ignore the other ways you might go to jail.) 6. If you roll two dice, the probability that one of the dice is a 3 and the other is not a 3 is: X+ Explain the calculation with words. 7. + In Yahtzee, you roll five dice at the same time. If all five dice display the same number, you get to yell "Yahtzee!" and get 50 points. What are the chances you get to yell "Yahtzee!" after a roll? 8. You roll three dice and want to get a 6 on at least one of them. (a) Are the chances of this happening more than, less than, or equal to ½? (b) Are the chances of this happening more than, less than, or equal to:+1+ ? 6 6 6 9. (The Paradox of the Chevalier de Méré). In a gambling game, players bet on the event that in 4 rolls of a die, a 1 (called an "ace" here) would occur at least once. In another game, players bet on the event that in 24 rolls of a pair of dice, a double ace (that is, a 1 on both dice at the same time) would occur at least once. A French nobleman, the Chevalier de Méré, believed that both events had the same chances. He reasoned: 63 *If I have a chance of getting an ace on one roll, then in 4 rolls I have a 4xchance of getting an ace at least once. *If I have a chance of getting a double ace on one roll of a pair of dice, then in 24 rolls I have 36 a 24×chance of getting a double ace at least once. 36 3 However, the gamblers found that the first event was a bit more likely than the second. What is wrong with the Chevalier's reasoning? 10. If you roll three dice, what are the chances exactly one of them will be a 6?
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Macroeconomics Principles Applications And Tools
ISBN: 9780134089034
7th Edition
Authors: Arthur O Sullivan, Steven M. Sheffrin, Stephen J. Perez
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