Using the Simulating the Probability of a Head With a Fair Coin applet on the text CD or other software, simulate the flipping of a balanced coin.
a. Report the cumulative proportion of heads after (i) 10 flips, (ii) 100 flips, (iii) 1000 flips, and (iv) 10,000 flips. Explain how the results illustrate the law of large numbers and the long-run relative frequency definition of probability.
b. Using the Simulating the Probability of Rolling a 3 or 4 applet or other software, simulate the roll of a die with a success defined as rolling a 3 or 4, using (i) 10 rolls, (ii) 100 rolls, (iii) 1000 rolls, and (iv) 10,000 rolls. Summarize results.