coinflips.py

#  coinflips.py
#  a program to test the concept presented at
#  http://www.khanacademy.org/math/probability/v/dependent-probability-example-1
#  by Daniel Veazey <danielveazey@gmail.com>

import random

#  what happens when you flip a coin a number of times, depending on
#  whether the coin is fair or unfair (weighted)
#  a pseudo-random number is genereated from 1 to 100
#  and compared to what its odds of landing on heads are
#  return 1 for heads if result is below odds
#  or return 0 for tails if the result is above the odds
def flipping(how_many_flips, odds):
    no_of_heads = 0
    for flip in range(0, how_many_flips):
        flip_result = random.randint(1, 100)
        if flip_result <= odds:
            no_of_heads += 1
    if no_of_heads == how_many_flips:
        return 1
    else:
        return 0

#  choosing a coin pseudo-randomly
#  pseudo-random integer is generated from the number of coins available
#  and compared to the number of fair coins available
#  return "unfair" if it is above the number of fair coins
#  or return "fair" if it is equal to or less than number of fair coins
def choosing_coin(how_many_fair, how_many_unfair):
    total_coins = how_many_fair + how_many_unfair
    chosen_coin = random.randint(1, total_coins)
    if chosen_coin > how_many_fair:
        return "unfair"
    else:
        return "fair"

#  ask user for parameters of test
print "Testing probability of fair and unfair coin flips when a random coin is pulled from a bag.\n"
fair_coins = float(raw_input("How many fair coins do you wish to put in the bag? "))
unfair_coins = float(raw_input("How many unfair coins do you wish to put in the bag? "))
unfair_odds = float(raw_input("For the unfair coins, what percent chance does one flip have that it will come up heads? "))
number_of_flips = float(raw_input("How many times do you want to flip the coin chosen from the bag? "))
#  tell the user what the probability is
print "\nThe chances of getting", int(number_of_flips), "heads in a row are about", float("%.4f" % ((((unfair_odds / 100.00) ** number_of_flips) * unfair_coins / (fair_coins + unfair_coins)) + ((.50 ** number_of_flips) * fair_coins / (fair_coins + unfair_coins))))*100.00, "percent."
print "I am now running the simulation 100,000 times. This may take a few seconds.\n"
#  the simulation: success is the number of times the flips came up all heads
success = 0
for x in range(100000):
    #  choose a coin
    if choosing_coin(fair_coins, unfair_coins) == "unfair":
        #  flipping an unfair coin
        if flipping(int(number_of_flips), (unfair_odds)) == 1:
            success += 1
    #  flipping a fair coin
    else:
        if flipping(int(number_of_flips), 50) == 1:
            success += 1
print "Simulation complete. All heads came up", success, "out of 100,000 times."