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Statistics

Probability Calculator

P(A and B), P(A or B). Free online Probability Calculator. Calculate probability online — fast, accurate, mobile-friendly, no signup needed.

Independent events: P(A ∩ B) = P(A)·P(B).
P(A and B) (indep)
0.15
P(A or B)
0.65

Derivation

  1. ├── 01GivenA = 0.3, B = 0.5
  2. ├── 02FormulaP(A and B) (indep): e.A × e.B
  3. ├── 03Substitutee.0.3 × e.0.5
  4. ├── 04Compute P(A and B) (indep)0.15
  5. ├── 05FormulaP(A or B): t+a-t × a
  6. └── 06Compute P(A or B)0.65
Did you know?

Probability theory traces to the Pascal–Fermat letters (1654) about a gambling dispute over how to fairly split a prize if a game is interrupted.

§01What is

Understanding the Probability Calculator

The Probability Calculator computes P(A and B) (indep) from 2 inputs: p(a), p(b). P(A and B), P(A or B).

Statistics is how we make sense of noisy real-world data. Whether you’re analysing survey results, sports scores, or business metrics, a statistics calculator gives you the exact formula-based answer so you can focus on the interpretation. The Probability Calculator sits in that toolkit — it P(A and B), P(A or B). Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

P(A and B) (indep) = e.A × e.B | P(A or B) = t+a-t × a

Where

A
P(A)
B
P(B)
P(A and B) (indep)
Output value
P(A or B)
Output value
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: P(A) = 0.3, P(B) = 0.5.

  1. 01Start by noting the input — P(A): 0.3.
  2. 02Start by noting the input — P(B): 0.5.
  3. 03Substitute these values into the formula: P(A and B) (indep) = e.A × e.B | P(A or B) = t+a-t × a
  4. 04Compute P(A and B) (indep): the calculator returns 0.15.
  5. 05Compute P(A or B): the calculator returns 0.65.
  6. 06Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Probability Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

P(A) halved

A = 0.15 (from 0.3)

Keep every other input at its default and halve the p(a). See how p(a and b) (indep) responds.

  1. 01New P(A): 0.15
  2. 02Baseline P(A and B) (indep): 0.15
  3. 03New P(A and B) (indep): 0.075
  4. 04P(A and B) (indep) decreases by 50% → use this sensitivity to plan for real-world variation.
02 · PATTERN

P(A) doubled

A = 0.6 (from 0.3)

Keep every other input at its default and double the p(a). See how p(a and b) (indep) responds.

  1. 01New P(A): 0.6
  2. 02Baseline P(A and B) (indep): 0.15
  3. 03New P(A and B) (indep): 0.3
  4. 04P(A and B) (indep) increases by 100% → use this sensitivity to plan for real-world variation.
03 · PATTERN

P(B) halved

B = 0.25 (from 0.5)

Keep every other input at its default and halve the p(b). See how p(a and b) (indep) responds.

  1. 01New P(B): 0.25
  2. 02Baseline P(A and B) (indep): 0.15
  3. 03New P(A and B) (indep): 0.075
  4. 04P(A and B) (indep) decreases by 50% → use this sensitivity to plan for real-world variation.
04 · PATTERN

P(B) doubled

B = 1 (from 0.5)

Keep every other input at its default and double the p(b). See how p(a and b) (indep) responds.

  1. 01New P(B): 1
  2. 02Baseline P(A and B) (indep): 0.15
  3. 03New P(A and B) (indep): 0.3
  4. 04P(A and B) (indep) increases by 100% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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