I. When rolling a pair of dice, the sum of the value shown on each die is either 2,3,4,5,6,7,8,9,10,11, or 12. Each of you have the game board on the previous page and 10 counters. The game is played by placing the 10 counters on any combination of numbers (you may place more than one counter on 1 number). One player rolls the dice. If the sum of the dice shown is one of the numbers you have chosen, you may remove that counter. (Only one counter removed at a time.) The object of the game is to be the first to remove all the counters from your game board.
1) Divide into groups of 4 and play the game for 15 min. Before the first roll of each game, make sure you have recorded your strategy to win. More specifically, which numbers did you cover, and how many counters did you place on each number.
2) After playing the game for 15 minuets, stop and discuss your results. Review your and your opponents strategies. How did they change?
3) As a group, determine the "ultimate strategy" to win. This strategy will be used in a game against the other groups in the class.
II. As the game progressed, each of you changed your strategy in relation to how many times a certain number was rolled.
1) Discussion. If the dice were rolled 25 times, which number would you think would show up the most number of times? The second most? Third most? Etc.
2) Test this in your groups. Every group needs to roll the dice 25 times. Keep a tally sheet on the back of the game board.
3) Record your results on the board along with the other groups.
4) Do the results of the multiple trials agree with your prediction? If not, make a new prediction.
III. The probability of an event occurring is the ratio of the number of desirable events and the total number of events.
2) Using this probability, how many of each outcome could you expect if you rolled the dice 100 times. Compare this result to part II number 3.
3) Now with all this powerful data at hand, decide an "ultimate strategy" to win the game in part I.