This applet simulates the experiment of tossing four times a coin and computes the frequency of ocurrence of the five possible outcomes (independently of order): [list] [*] Tail-Tail-Tail-Tail [*] Tail-Tail-Tail-Head [*] Tail-Tail-Head-Head [*] Tail-Head-Head-Head [*] Head-Head-Head-Head [/list] The coin can be a rigged one, having probability of landing on the head equal to [math]p[/math].
Choose a probability ([math]p=0.5[/math] corresponds to a balanced coin), click on [i]Initialisation[/i] to set up the simulation and then to [i]Start[/i]. To end the simulation click on [i]Stop[/i]. The binomial distribution is shown in red, while the simulated distribution appears in blue. See how an increase in the number of experiments results in a better approximation of the binomial distribution by means of the distribution of frequencies.