mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-10-06 13:49:30 +00:00
41 lines
1.5 KiB
Python
41 lines
1.5 KiB
Python
|
"""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))
|