# Long Run Probability

- Author:
- Jennifer Silverman, IM 6 – 8 Math

- Topic:
- Probability

1. Mai is playing a game where she will win only if she rolls a 1 or a 2 with a standard number cube.
a. List the outcomes in the sample space for rolling the number cube.
b. What is the probability Mai will win the game? Explain or show your reasoning.
c. If Mai is given the option to flip a coin and win if it comes up heads, is that a better option to win?
This applet displays a random number from 1 to 6, like a number cube. Mai won with the numbers 1 and 2, but you can choose any two numbers from 1 to 6. Record them in the boxes in the center of the applet.
2. Click the Roll button for 10 rolls, and then answer the questions below.
a. If the roll stops on one of your winning numbers, what happens in the table?
b. What appears to be happening with the points on the graph?
c. After 10 rolls, what fraction of the total rolls were a win?
3. How close are your answers for the probability of Mai winning and the fraction of wins after 10 rolls?
Roll the number cube 10 more times to fill in the table and graph the results, for a total of 20 points on the graph.
4. After 20 rolls, what fraction of the total rolls were a win?
5. How close are your answers for the probability of Mai winning and the fraction of wins after 20 rolls?