Problem: The long run but not the short run. Our intuition about chance behavior is not very accurate. In particular, we tend to expect that the long-run pattern described by probability will show up in the short run as well. For example, we tend to think that tossing a coin 20 times will give close to 10 heads.

Required:

(i) Set the probability of heads in the Probability applet to 0.5 and the number of tosses to 20. Click "Toss" to simulate 20 tosses of a balanced coin. What was the proportion of heads?

(ii) Click "Reset" and toss again. The simulation is fast, so do it 25 times and keep a record of the proportion of heads in each set of 20 tosses. Make a stemplot of your results. You see that the result of tossing a coin 20 times is quite variable and need not be very close to the probability 0.5 of heads.