# Law of Averages Applet - Activities

Author(s):
Kady Schneiter (Utah State University)

Coin Activity

Select the 'coin' radio button on the applet. Press the 'Get data' button to toss the coin 10000 times, do this several times so the results of a number of experiments are overlain in the plot. Use the plots to respond to the prompts below.

1. Move between the plot display radio buttons ('show %heads' et al.) as needed to answer the following questions.

• Are you more likely to get more than 60% heads in 10 tosses or 1000 tosses of a coin? Explain.
• Are you more likely to get more than 40% heads in 10 tosses or 1000 tosses of a coin? Explain.
• Are you more likely to get between 60% and 40% heads in 10 tosses or 1000 tosses of a coin? Explain.

2. Are you more likely to get exactly 50% heads in 10 tosses or 1000 tosses of a coin? Explain.

Die Activity

Select the 'die' radio button on the applet. Press the 'Get data' button to roll the die 10000 times, do this several times so the results of a number of experiments are overlain in the plot. Use the plots to respond to the prompts below.

1. Move between the plot display radio buttons ('show %threes' et al.) as needed to answer the following questions.

• Are you more likely to have at least 10 more than the expected number of threes for 100 rolls or 1000 rolls?
• Are you more likely to be within 5% of the expected percentage of threes for 100 rolls or 1000 rolls?

2. Are you more likely to get exactly the expected percentage of threes in 10 rolls or 1000 rolls of a die? Explain.

Kady Schneiter (Utah State University), "Law of Averages Applet - Activities," Convergence (June 2010), DOI:10.4169/loci003491