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  4. Probability Calculator

Probability Calculator

Independent two-event probabilities, solver, series of trials, normal range area, simple favorable/total, and Bayes.

Statistics

  • Average Calculator
  • Mean, Median, Mode, Range Calculator
  • Statistics Calculator
  • Standard Deviation Calculator
  • Number Sequence Calculator
  • Probability Calculator
  • Permutation and Combination Calculator
  • Sample Size Calculator
  • Z-score Calculator
  • Confidence Interval Calculator
  • P-value Calculator

How it works

Independent joints multiply; unions use inclusion-exclusion. Normal areas use standardized z-scores and Φ.

P∩=P(A)P(B) · P∪=P(A)+P(B)−P∩ · Φ((x−μ)/σ)

When to use

Use this tool when you need to: try two events at 0.5, XOR with 0.65 & 0.349, or normal μ=68 σ=4 from 60 to 72 (~81.9%).

How to use this tool

  1. Enter your values in the fields above.
  2. Review the formula and any mode options for your problem.
  3. Read the result and the step-by-step solution.

Try two events at 0.5, XOR with 0.65 & 0.349, or normal μ=68 σ=4 from 60 to 72 (~81.9%).

Frequently asked questions

What is the Probability Calculator?
Independent joints multiply; unions use inclusion-exclusion. Normal areas use standardized z-scores and Φ.
How do I use the Probability Calculator?
Enter the required values, then calculate. The Probability Calculator shows results, formulas, and step-by-step work when available. No account is required.
What formula does the Probability Calculator use?
P∩=P(A)P(B) · P∪=P(A)+P(B)−P∩ · Φ((x−μ)/σ)

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Probability calculator

Two independent events (union, intersection, XOR), a solver from any two knowns, series of trials, normal curve areas, simple favorable/total, and Bayes.

Calculator

Enter P(A) and P(B) between 0 and 1 for independent events. Computes complements, intersection, union, exclusive OR, and neither.

Try an example

How it works

What is probability?

Probability measures how likely an event is, as a number from 0 (impossible) to 1 (certain). In the simple case it is desired outcomes over total outcomes. Combinations of events further depend on independence, mutual exclusivity, or conditionals.

Two independent events

Complement P(A′)=1−P(A). Independent intersection P(A∩B)=P(A)P(B). Inclusive union P(A∪B)=P(A)+P(B)−P(A∩B). Exclusive OR P(AΔB)=P(A)+P(B)−2P(A∩B). Neither is 1−P(A∪B). The solver fills the same list from any two consistent knowns.

Normal distribution

A normal curve is shaped by mean μ and standard deviation σ. Convert bounds to z=(x−μ)/σ and use Φ(z) for area. Example: μ=68, σ=4, between 60 and 72 → z from −2 to 1 → about 81.9%. Confidence bands ±zσ around μ are large-sample known-σ approximations.

Bayes and dependence

When draws are without replacement (or otherwise dependent), use conditionals: P(A∩B)=P(A)P(B|A). Bayes updates a prior P(A) with likelihood P(B|A) and evidence P(B) to get posterior P(A|B).

Related calculators

Probability, counting, sampling design, and normal-based inference tools work together. Descriptive statistics calculators help when you start from raw data.

  • Permutation and Combination Calculator
  • Sample Size Calculator
  • Z-score Calculator
  • Confidence Interval Calculator
  • P-value Calculator
  • Statistics Calculator