Use the Simulating the Probability of Head with a Fair Coin applet on the text CD or other software to illustrate the long-run definition of probability by simulating short-term and long-term results of flipping a balanced coin.
a. Set the sample size to n = 10. Run the applet 10 times, and record the cumulative proportion of heads for each of the 10 simulations.
b. Now set the sample size n = 100. Run the applet 10 times, and record the 10 cumulative proportions of heads for the separate sets. Do they vary much?
c. Now set n = 1000. Run the applet 10 times, and record the 10 cumulative proportions of heads. Do they vary more, or less, than the proportions in part b based on n = 100?
d. Summarize the effect of the number of trials n on the variability of the proportion. How does this reflect what’s implied by the law of large numbers?