1. Mai is playing a game where she will win only if she rolls a 1 or a 2 with a standard number cube.[br][br] a. List the outcomes in the sample space for rolling the number cube.[br][br] b. What is the probability Mai will win the game? Explain or show your reasoning.[br][br] 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?[br][br]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.[br][br]2. Click the Roll button for 10 rolls, and then answer the questions below.[br][br] a. If the roll stops on one of your winning numbers, what happens in the table?[br][br] b. What appears to be happening with the points on the graph?[br][br] c. After 10 rolls, what fraction of the total rolls were a win?[br][br]3. How close are your answers for the probability of Mai winning and the fraction of wins after 10 rolls?[br][br]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.[br][br]4. After 20 rolls, what fraction of the total rolls were a win?[br][br]5. How close are your answers for the probability of Mai winning and the fraction of wins after 20 rolls?