probability calculator: method, formulas and interpretation

The probability calculator uses a dedicated calculation path for this exact problem rather than a generic input-and-output shell. Inputs are normalized before the formula is applied, and the result panel exposes the assumptions needed to audit the answer.

Event and conditional modes

The probability calculator keeps complement, independent AND, independent OR and conditional probability as separate models. Conditional mode requires a joint probability that cannot exceed either marginal event probability. Independent modes multiply the event probabilities because independence is an assumption supplied by the user.

Binomial count probabilities

The probability calculator also evaluates exactly, at most or at least k successes for n independent trials with constant success probability. It uses combination counts and sums the required terms rather than applying a normal approximation. Trials that change probability, depend on prior outcomes or stop early do not satisfy the binomial model.

Worked use and validation

The probability calculator rejects missing, non-finite or physically impossible values with a specific message. Load the worked example to inspect the complete calculation and compare it with a manual result before relying on a planning estimate.

How to read the output

The probability calculator separates the primary result from supporting quantities, unit conversions and limitations. Display rounding does not replace the unrounded values used inside later steps. Use consistent inputs and preserve the stated model when comparing scenarios.