binomial_distribution.py

"""For more information about the Binomial Distribution -
    https://en.wikipedia.org/wiki/Binomial_distribution"""


def binomial_distribution(successes: int, trials: int, prob: float) -> float:
    """

    Returns probability of k successes out of n tries,
    with p probability for one success

    The function uses the factorial function
    in order to calculate the binomial coefficient

    >>> binomial_distribution(3, 5, 0.7)
    0.30870000000000003

    >>> binomial_distribution (2, 4, 0.5)
    0.375

    """
    if successes > trials:
        raise ValueError("""successes must be lower or equal to trials""")
    if trials < 0 or successes < 0:
        raise ValueError("the function is defined for non-negative integers")
    if type(successes) != int or type(trials) != int:
        raise ValueError("the function is defined for non-negative integers")
    if prob > 1 or prob < 0:
        raise ValueError("prob has to be in range of 1 - 0")
    probability = (prob**successes)*(1-prob)**(trials-successes)
    # Calculate the binomial coefficient:
    # Calculate n! / k!(n-k)!
    coefficient = factorial(trials)
    coefficient /= (factorial(successes)*factorial(trials-successes))

    return probability * coefficient


# Implementation of the factorial function,
# used to calculate the binomial coefficient:
def factorial(n) -> int:
    """
    Factorial - The product of all positive integers less than or equal to n
    """

    if type(n) != int:
        raise ValueError("factorial(n) accepts only integer values")
    if n < 0:
        raise ValueError("factorial(n) works only for non-negative numbers")
    if n == 0:
        return 1
    result = 1
    for i in range(1, n+1):
        result *= i
    return result

if __name__ == "__main__":
    from doctest import testmod
    testmod()