Added a binomial distribution formula calculator algorithm

maths/binomial_distribution.py

@@ -0,0 +1,58 @@
+"""For more information about the Binomial Distribution -
+    https://en.wikipedia.org/wiki/Binomial_distribution"""
+
+
+def binomial_distribution(successes: int, trials: int, prob: float) -> float:
+    """
+
+    Returns 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 type(successes) != int or type(trials) != int:
+        raise ValueError("the function is defined for non-negative integers")
+    if prob > 1 or prob < 0:
+        raise ValueError("prob has to be in range of 1 - 0")
+    probability = (prob**successes)*(1-prob)**(trials-successes)
+    # Calculate the binomial coefficient:
+    # Calculate n! / k!(n-k)!
+    coefficient = factorial(trials)
+    coefficient /= (factorial(successes)*factorial(trials-successes))
+
+    return probability * coefficient
+
+
+# Implementation of the factorial function,
+# used to calculate the binomial coefficient:
+def factorial(n) -> int:
+    """
+    Factorial - The product of all positive integers less than or equal to n
+    """
+
+    if type(n) != int:
+        raise ValueError("factorial(n) accepts only integer values")
+    if n < 0:
+        raise ValueError("factorial(n) works only for non-negative numbers")
+    if n == 0:
+        return 1
+    result = 1
+    for i in range(1, n+1):
+        result *= i
+    return result
+
+if __name__ == "__main__":
+    from doctest import testmod
+    testmod()