"""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)
 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 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))