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Math & Numbers Runs in browser Updated 30 Mar 2026

Probability Calculator

Calculate single event, compound AND/OR, conditional, and Bayes theorem probabilities with formula display. Results as fractions, decimals, and percentages.

Favorable outcomes must be a non-negative integer less than or equal to total outcomes (total must be > 0).

Result

Enter values above to calculate the probability.

Formulae

P(A) = favorable outcomes / total outcomes

P(A AND B) = P(A) × P(B)   (independent)

P(A OR B) = P(A) + P(B) − P(A AND B)

P(A|B) = P(A∩B) / P(B)

Bayes: P(A|B) = P(B|A) × P(A) / P(B)
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How to use Probability Calculator

  1. Choose a probability type

    Select Single Event, Compound (AND/OR), Conditional, or Bayes Theorem from the tabs.

  2. Enter the required values

    Fill in favorable outcomes and total outcomes, or enter P(A) and P(B) values depending on the mode.

  3. View results in three formats

    The probability is displayed as a fraction, decimal, and percentage simultaneously.

  4. Read the formula

    The formula used for your selected mode is shown below the inputs so you can follow the calculation.

Probability Calculator FAQ

What is probability?
Probability measures the likelihood of an event occurring, expressed between 0 (impossible) and 1 (certain). P(A) = favorable outcomes / total outcomes.

How do I calculate the probability of two events both happening?
For independent events: P(A and B) = P(A) × P(B). For dependent events: P(A and B) = P(A) × P(B|A).

How do I calculate the probability of either event happening?
P(A or B) = P(A) + P(B) − P(A and B). For mutually exclusive events where both can't happen: P(A or B) = P(A) + P(B).

What is conditional probability?
P(A|B) is the probability of A given that B has already occurred. Formula: P(A|B) = P(A and B) / P(B).

What is Bayes theorem?
Bayes theorem reverses conditional probability: P(A|B) = [P(B|A) × P(A)] / P(B). It updates a prior probability given new evidence.

What is the difference between independent and dependent events?
Independent events don't affect each other — a coin flip doesn't affect the next. Dependent events do — drawing a card changes remaining probabilities.

How is probability expressed?
As a fraction (1/4), decimal (0.25), or percentage (25%). All three are shown simultaneously in this calculator.

What is complementary probability?
P(not A) = 1 − P(A). If the probability of rain is 0.3, the probability of no rain is 0.7.

Can I use this for dice or card problems?
Yes. Use single-event mode: enter favorable outcomes (e.g. 1 for rolling a 6) and total outcomes (e.g. 6 sides).

Is any data sent to a server?
No. All calculations run entirely in your browser. Nothing is uploaded or stored.

Background

Solve probability problems across four modes in one tool. Single-event probability calculates P(A) from favorable and total outcomes. Compound probability handles AND (intersection) and OR (union) for both independent and dependent events. Conditional probability computes P(A|B) — the probability of A given that B has occurred. Bayes theorem mode takes P(B|A), P(A), and P(B) as inputs and calculates the posterior probability P(A|B) — the foundation of probabilistic reasoning and machine learning. Each mode displays the formula used and results as a fraction, decimal, and percentage simultaneously. Ideal for statistics courses, data science students, competitive math, and everyday probability questions like coin flips, card draws, and dice rolls. All processing runs in your browser.

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