This game is called “Get Negative”. Roll two dice (record these in the order you roll them), and then do then do the following: take the first number rolled and subtract 2 times the second number rolled. Regardless of who rolls, Player A gets 3 points if the product is greater than or equal to 0 (i.e. it is zero or positive); Otherwise Player B gets 1 points. The players may or may not take turns rolling the dice as it does not matter who is rolling. Any player may score on any roll, and every roll will result in a score. Play the game by rolling the dice 25 times. For each turn, keep a record of both dice and the resulting answer and the points scored, according to the rules above. Tally the points and calculate the final score for each player. Remember, someone gets a point for each turn, depending on the numbers rolled. (One does not have to be rolling to receive the points.) (Note: you may test the game by yourself by doing all of the 25 rolls yourself and just giving the points to the appropriate player, A or B, or you may play the game with another person (one as player A and the other as player B) with each of you taking turns to roll a total of 25 times and giving the points on each roll to the appropriate player, A or B, according to the rules above). Expand and use the following to keep track: Numbers rolled: (List what is on both dice, in ordered rolled) Outcomes: (1st number minus two times second number) Player A (Points) Player B (Points) (Show all 25 rolls) Total score/# of rolls Using the data collected, answer each of the following questions: Compute the empirical (experimental) probabilities for each player, and explain how you found these probabilities. Player A: Player B: Explanation: Empirically, is this game fair? Answer this question yes or no. Show the mathematical work needed to support your answer, and explain what the numbers tell you using correct statistical vocabulary. Answer: Mathematical Justification: Explanation:
This game is called “Get Negative”. Roll two dice (record these in the order you roll them), and then do then do the following: take the first number rolled and subtract 2 times the second number rolled. Regardless of who rolls, Player A gets 3 points if the product is greater than or equal to 0 (i.e. it is zero or positive); Otherwise Player B gets 1 points. The players may or may not take turns rolling the dice as it does not matter who is rolling. Any player may score on any roll, and every roll will result in a score.
Play the game by rolling the dice 25 times. For each turn, keep a record of both dice and the resulting answer and the points scored, according to the rules above. Tally the points and calculate the final score for each player. Remember, someone gets a point for each turn, depending on the numbers rolled. (One does not have to be rolling to receive the points.) (Note: you may test the game by yourself by doing all of the 25 rolls yourself and just giving the points to the appropriate player, A or B, or you may play the game with another person (one as player A and the other as player B) with each of you taking turns to roll a total of 25 times and giving the points on each roll to the appropriate player, A or B, according to the rules above). Expand and use the following to keep track:
| Numbers rolled: (List what is on both dice, in ordered rolled) | Outcomes: (1st number minus two times second number) | Player A (Points) | Player B (Points) |
| (Show all 25 rolls) | |||
| Total score/# of rolls |
Using the data collected, answer each of the following questions:
Compute the empirical (experimental)
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Player A:
Player B:
Explanation: |
Empirically, is this game fair? Answer this question yes or no. Show the mathematical work needed to support your answer, and explain what the numbers tell you using correct statistical vocabulary.
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Answer: Mathematical Justification:
Explanation: |
Create a
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Sample Space:
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Compute the classical (theoretical) probabilities for each player, and explain how you found these probabilities.
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Player A:
Player B:
Explanation:
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Classically, is this game fair? Answer this question yes or no. Show the mathematical work needed to support your answer, and explain what the numbers tell you using correct statistical vocabulary.
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Answer:
Mathematical Justification:
Explanation:
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A game can only be classified as either fair or not fair – it cannot be both at the same time. How would you classify this game? Is it fair or not fair? Explain which group of information, classical or empirical, should carry more weight when deciding if the game is fair and explain why this is so.
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Answer:
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Given
a)
Two dice are rolled 25 times and we find the number on first dice minus two times the number on second dice. If the value is zero or greater than zero then A gets 3 points or else B gets 1 point. The numbers observed in 25 rolls and points scored are shown below
The total points of Player A
The total points of Player B
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