IM 7.8.4 Lesson: Estimating Probabilities Through Repeated Experiments
Locate and label these numbers on the number line by dragging the points.
Choose one of the numbers from the previous question. Describe a game in which that number represents your probability of winning.
Mai plays a game in which she only wins if she rolls a 1 or a 2 with a standard number cube.
- List the outcomes in the sample space for rolling the number cube.
- What is the probability Mai will win the game? Explain your reasoning.
- 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?
- Begin by dragging the gray bar below the toolbar down the screen until you see the table in the top window and the graph in the bottom window. 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. Click the Roll button for 10 rolls and answer the questions.
What appears to be happening with the points on the graph?
After 10 rolls, what fraction of the total rolls were a win?
How close is this fraction to the probability that Mai will win?
Roll the number cube 10 more times. Record your results in the table and on the graph from earlier.
After 20 rolls, what fraction of the total rolls were a win?
How close is this fraction to the probability that Mai will win?
For each situation, do you think the result is surprising or not? Is it possible? Be prepared to explain your reasoning.
You flip the coin once, and it lands heads up.
You flip the coin twice, and it lands heads up both times.
You flip the coin 100 times, and it lands heads up all 100 times.
If you flip the coin 100 times, how many times would you expect the coin to land heads up? Explain your reasoning.
If you flip the coin 100 times, what are some other results that would not be surprising?
You’ve flipped the coin 3 times, and it has come up heads once. The cumulative fraction of heads is currently . If you flip the coin one more time, will it land heads up to make the cumulative fraction ?