Mai plays a game in which she only wins if she rolls a 1 or a 2 with a standard number cube.

1. List the outcomes in the sample space for rolling the number cube.
2. What is the probability Mai will win the game? Explain your reasoning.

3. If Mai is given the option to flip a coin and win if it comes up heads, is that a better option for her to win?

4. With your group, follow these instructions 10 times to create the graph.

   • One person rolls the number cube. Everyone records the outcome in the table.

   • Calculate the fraction of rolls that are a win for Mai so far. Approximate the fraction with a decimal value rounded to the hundredths place. Record both the fraction and the decimal in the last column of the table.

   • On the graph, plot the number of rolls and the fraction of games that are wins.

   • Pass the number cube to the next person in the group so they can repeat these steps.

   roll	outcome	total number of wins for Mai	fraction of games played that are wins
   1
   2
   3
   4
   5
   6
   7
   8
   9
   10

   

   A blank coordinate grid with the origin labeled “O.” The horizontal axis is labeled “number of rolls” and the numbers 1 through 20 are indicated. The vertical axis is labeled “fraction of games played that are wins” and the numbers 0 through 1, in increments of zero point 1, are indicated.

5. Describe how the graph changes as the number of rolls increases.
6. 1. After 10 rolls, what fraction of the total rolls are a win?
   2. How close is this fraction to the probability that Mai will win?
7. Roll the number cube 10 more times. Record your results in this table and on the graph from earlier.

   roll	outcome	total number of wins for Mai	fraction of games played that are wins
   11
   12
   13
   14
   15
   16
   17
   18
   19
   20

8. 1. After 20 rolls, what fraction of the total rolls are wins?
   2. How close is this fraction to the probability that Mai will win?