coinflips_with_decimals.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, decimal

#  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 True for heads if result is below odds
#  or return False 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
    return no_of_heads == how_many_flips

#  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
#  True = unfair coin; False = fair coin
def choosing_coin(how_many_fair, how_many_unfair):
    total_coins = how_many_fair + how_many_unfair
    chosen_coin = random.randint(1, total_coins)
    return chosen_coin > how_many_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 = decimal.Decimal(raw_input("How many fair coins do you wish to put in the bag? "))
unfair_coins = decimal.Decimal(raw_input("How many unfair coins do you wish to put in the bag? "))
unfair_odds = decimal.Decimal(raw_input("For the unfair coins, what percent chance does one flip have that it will come up heads? "))
number_of_flips = decimal.Decimal(raw_input("How many times do you want to flip the coin chosen from the bag? "))

#  tell the user what the probability is
probability = decimal.Decimal((((((unfair_odds / decimal.Decimal('100.00')) ** number_of_flips) * unfair_coins / (fair_coins + unfair_coins)) + ((decimal.Decimal('.50') ** number_of_flips) * fair_coins / (fair_coins + unfair_coins))))*decimal.Decimal('100.00')).quantize(decimal.Decimal('.01'))
print "\nThe chances of getting", int(number_of_flips), "heads in a row are about", probability, "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) == True:
        #  flipping an unfair coin
        if flipping(int(number_of_flips), (unfair_odds)) == True:
            success += 1
    #  flipping a fair coin
    else:
        if flipping(int(number_of_flips), 50) == True:
            success += 1
print "Simulation complete. All heads came up", success, "out of 100,000 times."