Use the applet entitled Simulating the Probability of a Head with a Fair Coin to explore...

Use the applet entitled Simulating the Probability of a Head with a Fair Coin to explore the relationship between the proportion of heads on several flips of a coin and the theoretical probability of getting heads on one flip of a fair coin.

a. Repeat parts a–c of Applet Exercise 3.1 for the experiment of flipping a coin and the event of getting heads.

b. On the basis of your results for part a, do you believe that we could justifiably conclude that a coin is unfair because we flipped it 10 times and didn’t roll any heads? Explain.

Reference: Applet Exercise 3.1

Use the applet entitled Simulating the Probability of Rolling a 6 to explore the relationship between the proportion of sixes rolled on several rolls of a die and the theoretical probability of rolling a 6 on a fair die.

a. To simulate rolling a die one time, click on the Roll button on the screen while n = 1. The outcome of the roll appears in the list at the right, and the cumulative proportion of sixes for one roll is shown above the graph and as a point on the graph corresponding to 1. Click Reset and repeat the process with n = 1 several times. What are the possible values of the cumulative proportion of sixes for one roll of a die? Can the cumulative proportion of sixes for one roll of a die equal the theoretical probability of rolling a 6 on a fair die? Explain.

b. Set n = 10 and click the Roll button. Repeat this several times, resetting after each time. Record the cumulative proportion of sixes for each roll. Compare the cumulative proportions for n = 10 with those for n = 1 in part

a. Which tend to be closer to the theoretical probability of rolling a 6 on a fair die?

c. Repeat part b for n = 1,000, comparing the cumulative proportions for n = 1,000 with those for n = 1 in part a and for n = 10 in part b.

d. On the basis of your results for parts a, b, and c, do you believe that we could justifiably conclude that a die is unfair because we rolled it 10 times and didn’t roll any sixes? Explain.