Fix binomial distribution overflow for large trial counts

maths/binomial_distribution.py

@@ -1,8 +1,7 @@
 """For more information about the Binomial Distribution -
 https://en.wikipedia.org/wiki/Binomial_distribution"""
 
-from math import factorial
-
+from math import comb 
 
 def binomial_distribution(successes: int, trials: int, prob: float) -> float:
     """
@@ -26,9 +25,7 @@
     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)
+    coefficient = comb(trials, successes)
     return probability * coefficient
 
 

maths/test_binomial_distribution.py

@@ -0,0 +1,8 @@
+
+import pytest
+from maths.binomial_distribution import binomial_distribution
+
+def test_large_number_of_trials() -> None:
+    assert binomial_distribution(85, 171, 0.5) == pytest.approx(
+        0.060749764626165485
+    )