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"""For more information about the Binomial Distribution -
    https://en.wikipedia.org/wiki/Binomial_distribution"""
from math import factorial
def binomial_distribution(successes: int, trials: int, prob: float) -> float:
    Return 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)
    >>> binomial_distribution (2, 4, 0.5)
    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 not isinstance(successes, int) or not isinstance(trials, int):
        raise ValueError("the function is defined for non-negative integers")
    if not 0 < prob < 1:
        raise ValueError("prob has to be in range of 1 - 0")
    probability = (prob ** successes) * ((1 - prob) ** (trials - successes))
    # Calculate the binomial coefficient: n! / k!(n-k)!
    coefficient = float(factorial(trials))
    coefficient /= factorial(successes) * factorial(trials - successes)
    return probability * coefficient
if __name__ == "__main__":
    from doctest import testmod
    testmod()
    print("Probability of 2 successes out of 4 trails")
    print("with probability of 0.75 is:", end=" ")
    print(binomial_distribution(2, 4, 0.75))

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