Consider the following three games Game 1: Two six-sided dice (with numbers 1, 2
ID: 3331452 • Letter: C
Question
Consider the following three games Game 1: Two six-sided dice (with numbers 1, 2, 3, 4, 5, 6) are rolled. You get a point if the sum is even; your partner gets a point if the sum is odd. The first player to reach 5 points wins Game 2: Again, two six-sided dice are rolled. This time you get a point if the product is even; your partner gets a point if the product is odd. The first player to reach 5 points wins. Game 3: Again, two-six sided dice are rolled. If the sum of the two dice is 2, 7, or 12, you get 3 points. If the sum is anything else, you partner gets 1 point. The person yibt the highest point total after 10 rolls of the dice is the winner Before playing any of the games, determine who you think has the better chance of winning each game. Why do you think so? Use an online random generator (generate #s 1-6) or actual dice to play each game at least 10 times. Keep track of who wins. Compare your results with your thoughts in part A. a. b. d fair if each player has an equal probability of winning. Do you think the games are fair? Why do you think so? Analyze each of the three games. If the game is unfair, change the rules to make it fair Create two games, one which is fair and the other of which is unfair. Play each game several times to determine if what you expect to happen actually occurs d. e.Explanation / Answer
Answer to part a)
In game I , both have equal chances of winning
in game II , I have more chance of winning
In game III , my partner has more chance of winnin g( sum: 1,4,5,6,8,9,10,11 are the available options with the partner)
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Answer to part b)
The results I got are:
For game I: I win 6 times
For game II : I win 8 times , this is same as expected
For game III: the partner wins 9 times , this is same as expected
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Answer to part c & d)
Only Game I is fair because each partner has equal chance of winning
in Game II , Probability of sum even is : 27/36 = 0.75
Thus Game II is not fair
in game III, Probability of 2,3,7 or 12 = 11/36
hus again this game is unfair
the rule of this game ca be changed as follows
A wins if he gets sum between 2 to 6 , and B wins if he gets sum between 8 to 12
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