
"""simple docstring"""




from math import factorial



def 						lowercase_      (       A__			,		A__			,		A__		)							->							float:
    """simple docstring"""

    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(A__			,		A__		) or not isinstance(A__			,		A__		):
        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"		)
    snake_case								= (prob**successes) * ((1 - prob) ** (trials - successes))
    # Calculate the binomial coefficient: n! / k!(n-k)!
    snake_case								= float(factorial(A__		)		)
    coefficient /= factorial(A__		) * 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))



from ....utils import logging


_A   =			logging.get_logger(__name__)







class 					lowerCamelCase		(  A_  ):





     def __init__(self				:   Tuple    ,   _A				:   Optional[int]    ,   _A				:   Tuple=None    ,   _A				:   Union[str, Any]=2_0_4_8       )						->						List[Any]:
         snake_case								= config.__dict__
         snake_case								= modal_hidden_size
         if num_labels:
             snake_case								= num_labels

