StatReasonProbability & Distributions
These tools work directly with a named probability model, such as the normal or binomial distribution, rather than a dataset you collected. Every page shows the modeled event, the sample space or parameter units, the tail direction, and a complement check, so the exact question being answered is always visible.
A probability calculated here is a property of the model you selected, not a real-world forecast guaranteed to be calibrated. These pages calculate bounds and PMF normalization directly, but whether the named distribution actually fits your real situation, and whether the underlying events are independent with a constant probability or rate, are left for you to judge.
Engines in this category
- Normal Distribution Calculator
Convert normal-distribution values to areas, or areas to values.
- Binomial Probability Calculator
Find the exact probability of a specific number of successes in n trials.
- Expected Value Calculator
Calculate a discrete expected value and its variability.
- Combinations and Permutations Calculator
Count unordered selections or ordered arrangements from a set.
- Probability Calculator
Apply the addition, multiplication, and complement rules to named events.
- Conditional Probability Calculator
Find P(A|B) directly from a joint probability and a conditioning event.
- Bayes Theorem Calculator
Update a prior probability with test sensitivity and specificity evidence.
- Discrete Distribution Calculator
Validate a custom PMF and summarize its mean, variance, and SD.
- Inverse Normal Calculator
Find the value at a given percentile of a normal distribution.
- Binomial Cumulative Probability Calculator
Find the probability of at most or at least a given number of successes.
- Poisson Probability Calculator
Model rare, independent event counts over a fixed exposure.
- t Distribution Calculator
Look up Student's t distribution's CDF or a critical value directly.
- Chi-Square Distribution Calculator
Look up the chi-square distribution's CDF or upper-tail probability directly.
- F Distribution Calculator
Look up the F distribution's CDF or upper-tail probability directly.