






"""simple docstring"""






from math import factorial



def 					_A			(__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'''							)
    SCREAMING_SNAKE_CASE_      :  Optional[int]    						=		(prob**successes) * ((1 - prob) ** (trials - successes))
    # Calculate the binomial coefficient: n! / k!(n-k)!
    SCREAMING_SNAKE_CASE_      :  Optional[int]    						=		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, 0.7_5))










"""simple docstring"""






from typing import TYPE_CHECKING

from ...file_utils import _LazyModule, is_tokenizers_available, is_torch_available
from ...utils import OptionalDependencyNotAvailable


UpperCAmelCase_   : str   			= {"""configuration_gpt_neox""": ["""GPT_NEOX_PRETRAINED_CONFIG_ARCHIVE_MAP""", """GPTNeoXConfig"""]}

try:
  if not is_tokenizers_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCAmelCase_   : Dict   			= ["""GPTNeoXTokenizerFast"""]

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCAmelCase_   : List[str]   			= [
      """GPT_NEOX_PRETRAINED_MODEL_ARCHIVE_LIST""",
      """GPTNeoXForCausalLM""",
      """GPTNeoXForQuestionAnswering""",
      """GPTNeoXForSequenceClassification""",
      """GPTNeoXForTokenClassification""",
      """GPTNeoXLayer""",
      """GPTNeoXModel""",
      """GPTNeoXPreTrainedModel""",
  ]


if TYPE_CHECKING:
  from .configuration_gpt_neox import GPT_NEOX_PRETRAINED_CONFIG_ARCHIVE_MAP, GPTNeoXConfig

  try:
    if not is_tokenizers_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .tokenization_gpt_neox_fast import GPTNeoXTokenizerFast

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_gpt_neox import (
        GPT_NEOX_PRETRAINED_MODEL_ARCHIVE_LIST,
        GPTNeoXForCausalLM,
        GPTNeoXForQuestionAnswering,
        GPTNeoXForSequenceClassification,
        GPTNeoXForTokenClassification,
        GPTNeoXLayer,
        GPTNeoXModel,
        GPTNeoXPreTrainedModel,
    )


else:
  import sys

  UpperCAmelCase_   : Tuple   			= _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)


