5.95 Simulate law of large numbers Using the Random Numbers web app (or other software), simulate the flipping of balanced and biased coins.

a. Report the proportion of heads after (i) 10 flips,

(ii) 100 flips, (iii) 1000 flips, and (iv) 10,000 flips.

(Select the Coin Flips tab in the app. You can read off the proportions from the graph that appears after you press Simulate in each case.) Explain how the results illustrate the law of large numbers and the longrun relative frequency definition of probability.

b. Use the Random Numbers web app to simulate the roll of 3 or 4 with a die, using (i) 10 rolls, (ii) 100 rolls,

(iii) 1000 rolls, and (iv) 10,000 rolls. (Hint: What is the probability of rolling a 3 or 4? Use this to set up a biased coin, where you identify rolling a 3 or 4 as flipping a head.) Summarize results.