4.6 Use the Probability applet. The idea of probability is that the proportion of heads in many tosses of a balanced coin eventually gets close to 0.5. But does the actual count of heads get close to one-half the number of tosses? Let’s find out. Set the “Probability of Heads” in the Probability applet to 0.5 and the number of tosses to 50. You can extend the number of tosses by clicking “Toss” again to get 50 more. Don’t click “Reset” during this exercise.

1. (a) After 50 tosses, what is the proportion of heads? What is the count of heads? What is the difference between the count of heads and 25 (one-half the number of tosses)?

2. (b) Keep going to 200 tosses. Again record the proportion and count of heads and the difference between the count and 100 (half the number of tosses).

3. (c) Keep going. Stop at 300 tosses and again at 400 tosses to record the same facts. Although it may take a long time, the laws of probability say that the proportion of heads will always get close to 0.5 and also that the difference between the count of heads and half the number of tosses will always grow without limit.