In Example 16, we estimated the probability of winning at least $20 in the game was 0.40. Meanwhile, we concluded analytically that the actual probability was 0.20.
a. Explain what caused the fairly large disparity between our estimated result and the actual result.
b. The simulation in the example consisted of 20 repetitions. Pick up where we left off in the random number table in the example, and conduct another 80 repetitions, for a total of 100. What is the estimated probability based on these 100 repetitions? Is it closer to the actual probability?
c. What should tend to happen to the difference between the actual and the estimated probabilities as the number of repetitions in the simulation increases?