statistics_bernouli_trials_and_similar.py

def algorithmic_chance_men_in_group(pop_size, sample_size, num_men): 
    """Used to estimate the odds of selecting `num_men` men out of
    a population of size `pop_size`, when taing a sample of size 
    `sample_size`
    
    Usage:
    >>> chance_as_percent = algorithmic_chance_men_in_group(30000, 1000, 600)[0]
    """
    # assuming that 50% of the pop is men 
    numerator = 1 
    denominator = 1 
    chance = decimal.Decimal('1.0') 
    total_men = pop_size // 2 
    total_women = total_men 
    # This is the chance that we get num_men men 
    for _ in range(num_men): 
        numerator *= total_men 
        denominator *= total_men + total_women 
        total_men -= 1 
    # and then this is the chance that we get (sample_size - num_men) women 
    # ...otherwise we'd have just the chance to have AT LEAST num_men men, 
    # ...not EXACTLY num_men men 
    for _ in range(sample_size - num_men): 
        numerator *= total_women 
        denominator *= total_men + total_women 
        total_women -= 1 
        
    # This factor is interesting!
    # We need to multiply by this, because otherwise, we just calculate the odds that
    # the first `num_men` people are men, and all the rest are women.
    # This factor accounts for all the other situations, which are equaly likely to happen, and
    # for our question, they should all be added up. To us, it doesn't matter if we got
    # all the men  first, then all the women, or men and women came in any order
    multiplier = math.factorial(sample_size) //math.factorial(num_men) //math.factorial(sample_size-num_men)
 
    # (chance_as_percent, numerator, denominator, correction_factor_because_of_permutation_effects)
    return numerator / denominator * multiplier * 100, numerator, denominator, multiplier 

 
def bernouli_chance_men_in_group(sample_size, num_men):
    """This function is used to test the correction of the first one.
    While the algorithmic function accounts for the fact that if we subtract an
    individual from the larger population, that somewhat decreases the chance that
    we'll meed a individual of the same sex, a bernouli trial assumes the chance is always 0.5
    
    The functions give nearly the same answer if the population is large enough
    """
    return (
      math.factorial(sample_size) // math.factorial(num_men) // math.factorian(sample_size - num_men) * 
      pow(0.5, sample_size
         )