Use this probability or sampling tool to compute a stated quantity or generate reproducible draws from a precisely parameterized distribution or stochastic model.

Successes

Required integer input.

Trials

Required integer input.

Calculate empirical probability from observed successes and trials. The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

Probability

The resulting probability returned as a number.

Percentage (%)

The resulting percentage returned as a number.

• Results depend on parameterization, support, random source, seed, convergence, burn-in, autocorrelation, proposal quality, normalization, numerical tails, and whether model assumptions match the process. Samples are not exact evidence of convergence.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

Check analytic moments or known test cases, use independent chains and diagnostics for Monte Carlo methods, report seed and effective sample size, and inspect tail behavior.

• Negative Binomial Distribution Sampler

  Draw the number of failures before a specified integer number of successes in independent Bernoulli trials.

• Probability Complement Calculator

  Calculate the complement of a probability.

• Expected Value Calculator

  Calculate the probability-weighted expected value of discrete outcomes.