Question

Question 1 In role-playing games, such as the original, Dungeons and Dragons, gamers use a variety of dice shapes, not just the standard cube. For example one version of a d10' has ten faces numbered 0,1,2,. .. ,9, and each face is equally likely to become the top face (the face that is read) when the die is 'thrown'. Suppose gamer Alice does not have one of these dice but does have a d6 (i.e. a regular cubic die with six faces labelled 1,2,. . .,6.) To simulate throwing one of these d10 dice, Alice throws her d6 twice, resulting in a pair of values (a, b) e S = {1, ,6)2. She then adds the two values and reduces the sum (if necessary) modulo 10. The result is a value v in [0,...,9), as required. 0 (a) Write out the partition of the sample space S comprising the ten events (v=0),(v=1), ,(v=9) (b) Find the probability of each of the ten events listed for part (a). (c) Alice's simulation method is not good. What are its worst features in your opinion? (d) Instead of adding the two values and reducing modulo 10, Alice could multiply thenm and reduce modulo 10. Would this method be better, or worse, than her adding method? Why?

Answer 1

2. 36 9 36 36

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So the multiplying method is worse than the adding method. Which can be clearly seen by calculating probabilities of all 9 events in both methods.