Access the Flipping Fair Coins applet. The experiment consists of tossing three fair coins and recording x, the number of heads.

a. Use the laws of probability to write down the simple events in this experiment.

b. Find the probability distribution for x. Display the distribution in a table and in a probability histogram.

c. Use the Flipping Fair Coins applet to simulate the probability distribution—that is, repeat the coin-tossing experiment a large number of times until the relative frequency histogram is very close to the actual probability distribution. Start by performing the experiment once (click) to see what is happening. Then speed up the process by clicking. Generate at least 2000 values of x. Sketch the histogram that you have generated.

d. Compare the histograms in parts b and c. Does the simulation confirm your answer from part b?