Discrete Probability Distributions Calculators
This page presents tools that summarise count-based outcomes using probability models, providing numerical results for variables with distinct possible values.
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Bernoulli Distribution Calculator
A single event with only two possible outcomes has a fixed chance of success and a fixed chance of failure.
Example use: estimating the chance that a tossed coin lands on heads once.
Inputs: probability of success
Outputs: probability, average outcome, spread of outcomes, typical deviation, outcome value, probability of that outcome
Visual: a simple bar showing the chance of each possible outcome
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Binomial Distribution Calculator
A repeated set of identical trials produces a distribution that depends on how many attempts are made and how likely success is each time.
Example use: counting how many times a fair die shows a six in several throws.
Inputs: number of trials, chance of success, probability type, number of successes, upper bound for successes, output type
Outputs: probability
Visual: a display showing the likelihood of each possible number of successes
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Discrete Uniform Distribution Calculator
A set of whole-number outcomes within a fixed range gives each value the same chance of occurring.
Example use: choosing a random whole number between two limits for a simple game.
Inputs: minimum value, maximum value, probability type, chosen value, upper bound
Outputs: probability
Visual: a set of equal-height bars showing the chance of each value in the range
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Geometric Distribution Calculator
A sequence of identical trials continues until the first success, creating a distribution based on how long the wait lasts.
Example use: counting how many attempts it takes to roll an even number on a die.
Inputs: chance of success, probability type, trial number, upper bound, output type
Outputs: probability
Visual: a bar display showing how the chance changes as the number of trials increases
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Hypergeometric Distribution Calculator
A fixed population with a known number of successes produces a distribution when a sample is taken without replacement.
Example use: drawing several coloured balls from a small bag without putting any back.
Inputs: population size, number of successes in the population, sample size, probability type, number of successes in the sample, upper bound
Outputs: step explanation, calculation process, outcome value, probability of that outcome
Visual: a display showing the probability for each possible number of successes in the sample
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Logarithmic Distribution Calculator
A distribution with many small counts and fewer large counts arises when the chance of an outcome decreases steadily as the count increases.
Example use: modelling how often a person repeats a simple action before stopping.
Inputs: shape value, observed count, output type
Outputs: probability of the count, step explanation, calculation process
Visual: a display showing how the probability decreases as the count grows
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Multinomial Distribution Calculator
A set of repeated trials with more than two possible outcomes produces a distribution based on the chance of each category.
Example use: recording how many times each face of a die appears after many throws.
Inputs: probabilities for each category, counts for each category
Outputs: total number of trials, multinomial probability
Visual: a comparison of expected and observed counts for each category
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Negative Binomial Distribution Calculator
A sequence of identical trials continues until a set number of successes occurs, producing a distribution for the number of failures along the way.
Example use: counting how many missed attempts occur before achieving several successful throws in a simple game.
Inputs: required number of successes, chance of success, probability type, number of failures, upper bound, output type
Outputs: probability, average outcome, typical deviation, number of failures, probability of that number
Visual: a display showing the chance of each possible number of failures
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Poisson Distribution Calculator
Events that occur independently at a steady average rate form a distribution describing how many events may happen in a fixed interval.
Example use: estimating how many birds might land in a garden during a short period.
Inputs: average event rate, probability type, number of events, upper bound, output type
Outputs: probability, event count, probability of that count
Visual: a display showing the likelihood of different event counts
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Skellam Distribution Calculator
The difference between two independent event counts with their own average rates forms a distribution centred on their expected difference.
Example use: comparing how many times two separate timers beep during the same period.
Inputs: first average rate, second average rate, probability type, difference value, upper bound, output type
Outputs: probability, average difference, spread of differences, difference value, probability of that difference
Visual: a display showing the chance of each possible difference
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Zipf Distribution Calculator
A ranked set of items where lower ranks occur more often than higher ranks forms a distribution that decreases steadily with rank.
Example use: modelling how often different whole numbers appear when smaller numbers are chosen more frequently.
Inputs: number of items, exponent value, probability type, rank, upper bound for rank, output type
Outputs: probability, normalisation constant, rank, probability of that rank
Visual: a display showing how the chance decreases as the rank increases
Discrete Distributions FAQs
A discrete probability distribution assigns likelihoods to variables with separate values, producing probabilities for each distinct outcome.
Discrete models describe countable outcomes, whereas continuous models represent values that fill entire intervals without gaps.
The Poisson distribution reflects rare event counts occurring at a constant average rate within a defined interval.
The total probability across all possible values equals 1, representing the full set of outcomes for the variable.