TheAlgorithms/Python · error · ValueError

the function is defined for non-negative integers

Error message

the function is defined for non-negative integers

What it means

In binomial_distribution, after the successes<=trials check, negative trials or successes raise ValueError('the function is defined for non-negative integers'). Counting experiments cannot have negative counts.

Source

Thrown at maths/binomial_distribution.py:23

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))

View on GitHub (pinned to f5988cc097)

Solutions

1. Validate trials >= 0 and successes >= 0 before calling.
2. Fix the subtraction that produced the negative count.
3. Reject negative inputs at the parse boundary with a clearer message.

Example fix

# before
p_x = binomial_distribution(k, n, 0.5)  # n may be negative

# after
if n < 0 or k < 0:
    raise ValueError(f"counts must be non-negative: k={k}, n={n}")
p_x = binomial_distribution(k, n, 0.5)

if trials < 0 or successes < 0:
    raise ValueError(f"counts must be non-negative: k={successes}, n={trials}")
p = binomial_distribution(successes, trials, prob)

def valid_binomial_counts(k: object, n: object) -> bool:
    return isinstance(k, int) and isinstance(n, int) and k >= 0 and n >= 0

When it happens

Trigger: binomial_distribution(-1, 5, 0.5); binomial_distribution(2, -4, 0.5); counts from deltas like trials = end - start where start > end.

Common situations: Negative counters from off-by-one loops; parsed user input with minus signs; reusing the same message for the type check below makes grepping ambiguous — read the line number.

Related errors

• successes must be lower or equal to trials
• prob has to be in range of 1 - 0
• Limit for the Catalan sequence must be ≥ 0
• Number should not be negative.
• Negative arguments are not supported

AI-assisted analysis of TheAlgorithms/Python@f5988cc097 (2026-08-14). Data as JSON: /api/errors/dfffa6de92bef7e7. Report an issue: GitHub.