Notice that the main program is complete, while the rest of the functions are merely stubbed out. The interface of each function has been defined, i.e. how many and what types of parameters are expected as well as what will be returned, but the functions have not yet been implemented. Comments have been included inside the function definitions as reminders for how we expect to implement them.
# This program computes the probability of rolling five of kind with # six-sided dice by running a series of simulations and computing # the average number of rolls required. def main(): printIntro() numTrials = input("Enter number of simulations to run: ") avg = simulate(numTrials) print "The average is:", avg print "The probabilty is:", 1/avg def printIntro(): """ Inputs: None Returns: None Purpose: To print an introduction to the user. """ return def simulate(n): """ Inputs: An integer n representing the number of simulations to run. Returns: A float representing the average number of rolls required to get five of a kind. Purpose: Simulate n trials of rolling dice and compute the average. """ # will call simulateOneTime n times return 100.0 def simulateOneTime(): """ Inputs: None Returns: An integer representing the number of rolls required to get five of a kind. Purpose: Simulate one trial and count the number of rolls. """ # will call rollDice until the result is allSame return 100 def rollDice(n): """ Inputs: An integer n representing the number of dice to roll. Returns: A list containing the dice rolls of length n. Purpose: Randomly roll n dice. """ # will call rollOne n times return  * n def allSame(ls): """ Inputs: A list of values. Returns: True if all the values in the list are the same. Otherwise False. Purpose: Checks whether the values in a list are equal. """ # will check that each value is equal to the first value return True def rollOne(): """ Inputs: None Returns: An integer representing the die value between 1 and 6. Purpose: Randomly roll one die. """ # will use the random library to simulate a die roll return 1 main()