



'''simple docstring'''





from math import factorial




def lowerCAmelCase  (__A  ,	__A  ,	__A):



     """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''')
     _a      =  (prob**successes) * ((1 - prob) ** (trials - successes))
     # Calculate the binomial coefficient: n! / k!(n-k)!
     _a      =  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))









def 					lowerCamelCase__       (						A__       :					list	):





       '''simple docstring'''



       __lowerCamelCase   =						len(A__	)
       for _ in range(A__	):
              for i in range(_ % 2  ,			arr_size - 1  ,			2	):
                     if arr[i + 1] < arr[i]:
                            __lowerCamelCase,   __lowerCamelCase   =						arr[i + 1], arr[i]

       return arr


if __name__ == "__main__":
       UpperCAmelCase_									=	list(range(10, 0, -1))
       print(f"""Original: {arr}. Sorted: {odd_even_transposition(arr)}""")

