Use the web app Random Numbers (go to the tab that says Coin Flips) on the book’s website or other software (such as random.org/coin) to illustrate the long-run definition of probability by simulating short term and long-term results of flipping a balanced coin. 

a. Keep the probability of a head at the default value of 50% and set the number of flips to generate in a simulation to 10. Click on Simulate and record the proportion of heads for this simulation. Do this a total of 10 times by repeatedly clicking Simulate.
b. Now set the number of flips to 100. Click Simulate 10 times, and record the 10 proportions of heads for each simulation. Do they vary much?
c. Now set the number of flips to 1000. Click Simulate 10 times, and record the 10 proportions of heads for each simulation. Do they vary more, or less, than the proportions in part b based on 100 flips?
d. Summarize the effect of the number of flips on the variability of the proportion. How does this reflect what’s implied by the law of large numbers?