MAT 1000 Worksheet 2 PG

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Wayne State University *

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1000

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Mathematics

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Jan 9, 2024

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pdf

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Probability and Games Module Worksheet 2 MAT 1000 Wayne State University The game that we are playing in this worksheet is Yahtzee. In Yahtzee, a small straight is when you roll 4 sequential dice (1,2,3,4 or 2,3,4,5 or 3,4,5,6), a large straight is when you roll 5 sequential dice (1,2,3,4,5 or 2,3,4,5,6), a 4 of a kind is when at least 4 of the dice have the same value (for example 2,2,2,2,5 or 2,2,2,2,6 or 2,2,2,2,2) and a Yahtzee is when all five dice show the same value (1,1,1,1,1 or 2,2,2,2,2 or 3,3,3,3,3 or 4,4,4,4,4 or 5,5,5,5,5 or 6,6,6,6,6). 1. You roll the following: a. What would you save to try to get a full house? I would save the 4, 4, 5, and 5 to try to get a full house. b. If you save the dice you listed above, what is the probability that you roll a full house in the next roll? 2/6 or ⅓. c. If you save the dice you listed in part a, what is the probability that you roll a full house in the next two rolls (rolling a die twice is like rolling 2 dice)? 2/12 2. You roll the following: a. What would you save if you were going to try to roll a 4 of a kind? I would save the 2, 2, and 2 and reroll the 4 and 5.
b. What is the probability that you get a 4 of a kind in your next roll if you save the dice listed in part a? 11/36 c. What is the probability that you get a Yahtzee in your next roll if you save the dice listed in part a? 1/36 d. If you instead wanted to go for a small or large straight, what would you save? I would save the 2, 4, and 5. e. If you save the dice listed in part d, what is the probability that you would get a small straight in the next roll? 11/36 f. If you save the dice listed in part d, what is the probability that you would get a large straight in the next roll? 2/36 or 1/18 g. Based on your answers above, what should you do if you roll the dice listed above? Explain your reasoning. I would save the 2, 4, and 5 and try to go for the large straight because it has the same probability as going for 4 of a kind, except a large straight is worth more points. 3. You roll the following: What should you do? Explain your reasoning. There is a ⅙ probability that you get a large straight is you save the 1, 2, 4, and 5 and reroll the 6 to try to get a 3.
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