TheAlgorithms/Python · error · ValueError

prob has to be in range of 1 - 0

Error message

prob has to be in range of 1 - 0

What it means

The final guard in binomial_distribution requires 0 < prob < 1 strictly; a probability of exactly 0, exactly 1, or anything outside raises ValueError('prob has to be in range of 1 - 0'). The implementation's probability formula assumes an interior probability.

Source

Thrown at maths/binomial_distribution.py:27

    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. Pass a strict interior probability (e.g. 1e-9 < p < 1 - 1e-9).
2. Laplace-smooth estimated probabilities: p = (successes + 1) / (trials + 2).
3. Divide percentages by 100 before calling.

Example fix

# before
p_x = binomial_distribution(k, n, 70)  # percent, not probability

# after
p = 70 / 100
p_x = binomial_distribution(k, n, p)

if not 0 < prob < 1:
    raise ValueError(f"prob must be strictly between 0 and 1, got {prob}")
p = binomial_distribution(successes, trials, prob)

def is_interior_probability(p: object) -> bool:
    return isinstance(p, (int, float)) and 0 < p < 1

When it happens

Trigger: binomial_distribution(2, 4, 1.0); binomial_distribution(2, 4, 0); binomial_distribution(2, 4, 1.5); prob computed as 1 - epsilon that rounds to exactly 1.0.

Common situations: Edge-case probabilities from degenerate data (all successes observed -> p estimated as 1.0); clamping code that snaps to [0,1] inclusive; user-entered percentages like 70 passed instead of 0.7.

Related errors

• successes must be lower or equal to trials
• the function is defined for non-negative integers
• 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/89354fd329bb30b0. Report an issue: GitHub.