Section 3: Case Study Roll The Dice

Transcription

1 Section 3: Case Study Roll The Dice Relates to Questions Time Allocated: 36 minutes. INTRODUCTION You have been playing a game in which the rules are as follows: Each game consists of 2 turns. o For each turn, roll one six-sided die 6 times, making a note of each number in the order it was rolled. o Once you have your list of six numbers, determine the possible scores for the turn according to the categories below. For each game, score the game by finding the highest possible combined score from the two turns, noting that no category may be used more than once (i.e. you may not score the two hands in the same category). As you have a keen interest in statistics, you have decided to simulate several games in Excel and analyze the resulting scores. Questions 20 to 26 require only the turn results. Questions 27 to 29 require analysis of the game results. The workbook provided contains dice rolls from 6,000 simulated turns (3,000 games). Use the rules below to first determine the possible scores for the turns, and then to find the highest possible score for each game. SCORING TURNS Category Criteria Score High and Often Any turn The highest number rolled in the turn multiplied by the number of times it was rolled that turn Summation Any turn Sum of all six dice rolls Highs and Lows Only two numbers Any turn The six rolls are all one of two numbers (e.g ) The highest number rolled multiplied by the lowest number rolled multiplied by the difference between them 30 All the numbers The rolls are (in any order) Ordered subset of four When listed in the order rolled the numbers contain a run of 4 consecutive increasing or decreasing numbers (e.g or ) 50 For Questions 20 to 27, select your answer from a multiple choice list. For Questions 28 to 29, you are required to type in your answer. Prepare your model and then use it to answer the given questions. When finished, please upload your workbook (Question 30).

2 QUESTIONS Question 20 If all turns were scored as High and Often what would the total score for all 6,000 turns be? A. 52,245 B. 52,246 C. 52,247 D. 52,248 E. 52,249 F. 52,250 G. 52,251 H. 52,252 I. 52,253 Question 21 What is the most common score that would be attained if all 6,000 turns were scored under the Summation category? A. 16 B. 17 C. 18 D. 19 E. 20 F. 21 G. 22 H. 23 I. 24

3 Question 22 What is the best possible score using the Highs and Lows category? A. 46 B. 47 C. 48 D. 49 E. 50 F. 51 G. 52 H. 53 I. 54 Question 23 In turns that qualify to be scored as Only Two Numbers how many threes were rolled in total? A. 127 B. 128 C. 129 D. 130 E. 131 F. 132 G. 133 H. 134 I. 135

4 Question 24 Looking at the turns in the order listed in the Workbook, which turn number is the 50 th turn to qualify for All The Numbers? A. 2,970 B. 2,971 C. 3,033 D. 3,148 E. 3,205 F. 3,260 G. 3,458 H. 3,620 I. 3,674 Question 25 How many turns qualify to be scored as Ordered Subset of Four? A. 94 B. 95 C. 96 D. 97 E. 98 F. 99 G. 100 H. 101 I. 102

5 Question 26 If all turns were scored according to their second highest scoring category, what would the total score for all the turns be? A. 126,783 B. 126,784 C. 126,785 D. 126,786 E. 126,787 F. 126,788 G. 126,789 H. 126,790 I. 126,791 Question 27 Grouping the turns into games, you can identify the highest game score achieved. How many of the 3,000 games achieve this maximum score? Remember that no scoring category may be used more than once per game. A. 4 B. 5 C.6 D. 7 E. 8 F. 9 G. 10 H. 11 I. 12

6 Question 28 What is the total score for all the games? Type in your answer, without any thousands separator (if relevant). E.g. 1,000,000 should be typed as Question 29 If the odd numbered games are played by Player 1, and the even numbered games are played by Player 2, and they are matched off against each other (e.g. game 1 vs game 2, game 3 vs game 4) what is the value of (Number of matches won by Player 1) minus (Number of matches won by Player 2)? Type in your answer, without any thousands separator (if relevant). E.g. 1,000,000 should be typed as

7 Answers 20 B 21 F 22 I 23 B 24 D 25 E 26 G 27 F n/a