CALCULATE WITH CONFIDENCE

Statistics · Probability

Dependent Events Calculator

Analyze two-stage dependent events using a first-stage probability and different second-stage probabilities under that event and its complement.

Statistics · Probability

Enter your statistical inputs

Private in-browser calculation · explicit assumptions
Follow each branch by multiplying conditional probabilities; add mutually exclusive terminal paths when the question combines them.
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example

Enter plain numbers without measurement units. Datasets accept commas, spaces, semicolons, or line breaks and are limited to 10,000 values. Results stay in this browser.

Statistics result

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Understand the probability

What the dependent events calculator is calculating

Following conditional branches. Conditional probability changes the reference group. A branch probability must be read inside the branch condition, while Bayes’ theorem reverses the conditioning direction using prior probabilities.

Probability rule

P(A∩B)=P(A)P(B|A); P(B)=P(A)P(B|A)+P(not A)P(B|not A).

Every probability must remain between 0 and 1, and overlapping regions must be jointly feasible. The calculator rejects combinations that violate the stated model.

How to interpret it

Different conditional probabilities quantify how the first event changes the second event’s modeled probability.

Model boundary: The inputs describe a complete binary partition A/not A and the same outcome B in both conditional branches.

Quick guide

How to use this calculator

  1. Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
  2. Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
  3. Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.

Calculation method

How the dependent events calculator works

P(A∩B)=P(A)P(B|A); P(B)=P(A)P(B|A)+P(not A)P(B|not A).

Different conditional probabilities quantify how the first event changes the second event’s modeled probability.

Worked example

Dependent Events example

P(A)=0.3, P(B|A)=0.8, and P(B|not A)=0.2 give P(A and B)=0.24 and P(B)=0.38.

P(A∩B)=P(A)P(B|A); P(B)=P(A)P(B|A)+P(not A)P(B|not A).

Supported inputs

Precision and limits

Model and design

The inputs describe a complete binary partition A/not A and the same outcome B in both conditional branches.

Numerical scope

Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.

Interpretation

Different conditional probabilities quantify how the first event changes the second event’s modeled probability.

Decision boundary

The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.

Privacy

Entered values and calculated results stay in this browser and are not sent to an analytics service.

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