Total Probability Calculator
Verified Calculation Engine
The online Total Probability Calculator helps you calculate instantly and solve problems related to Probability Advanced. This tool provides accurate results using standard formulas and step-by-step calculation; you can view the formula with example in the calculator where available. Whether you are a student, teacher, or professional, this calculator simplifies complex calculations and saves time. Enter the required values below and get instant results. Results are shown clearly, with optional step-by-step explanation where applicable. The tool is free to use and works in any modern browser—no download or installation required. Bookmark this page for quick access whenever you need reliable Math Numbers calculations.
Applies law of total probability: P(B) = Σ P(B|Aᵢ)·P(Aᵢ) where {Aᵢ} is a partition of sample space.
Law of total probability:
P(B) = Σᵢ P(B|Aᵢ)·P(Aᵢ)
where {Aᵢ} is a partition of sample space
Requires: Σ P(Aᵢ) = 1 and Aᵢ ∩ Aⱼ = ∅ for i ≠ j
Total probability using partition of sample space
Inputs
Results
Worked Examples
Example 1: Basic
Given P(A₁) = 0.3, P(A₂) = 0.7, P(B|A₁) = 0.8, P(B|A₂) = 0.2, find P(B)
- events: [ "A1", "A2" ]
- probabilities: [ 0.3, 0.7 ]
- conditionalProbabilities: [ 0.8, 0.2 ]
- totalProbability: 0.38
- contributions: 0.24, 0.14
Example 2: Board Level
Three machines produce items with probabilities 0.5, 0.3, 0.2 and defect rates 0.01, 0.02, 0.03. Find probability of defect.
- events: [ "Machine1", "Machine2", "Machine3" ]
- probabilities: [ 0.5, 0.3, 0.2 ]
- conditionalProbabilities: [ 0.01, 0.02, 0.03 ]
- totalProbability: 0.017
- contributions: 0.005, 0.006, 0.006
About this calculator
Overview
Total Probability Calculator evaluates Total Probability for the engineering-math / probability-random-variables library. Primary input cue: Event A Probability [required] — field id `event_a`. Method anchor: Probability/statistics formula evaluation for Total Probability.. Probability/statistics formulas (mean, variance, common PMF/PDF models, regression) evaluated .
When to use
Use this page when you need total probability from known inputs and want a transparent arithmetic or symbolic check.
Inputs explained
- Event A Probability [required] — field id `event_a`
- Event B Probability [required] — field id `event_b`
Formula / method
Probability/statistics formula evaluation for Total Probability.. Probability/statistics formulas (mean, variance, common PMF/PDF models, regression) evaluated for the distribution or sample inputs this calculator accepts. This page targets specifically: Total Probability (total probability) (calculator id: total-probability-calculator).
Worked example
Example path for Total Probability: set event_a = 3, event_b = 2. Then compare the on-page result with a hand calculation using: Probability/statistics formula evaluation for Total Probability.. Probability/statistics formulas (mean, variance, common PMF/PDF models, regression) evaluated for the distribution or sample inputs this calculator accepts. This page targets specifically: Total Probability (total probability)..
Interpreting results
If total probability looks implausible, re-check units and which field is optional vs required.
Assumptions
- The wired execution function for `total-probability-calculator` is the source of numerical behavior.
- Inputs for `total-probability-calculator` follow the on-page labels; values/shapes must match this operation.
- Matrix/vector shapes must match the operation implied by total probability.
Limitations
- Display rounding can differ slightly from a CAS/symbolic exact form of total probability.
- Edge cases outside the intended domain of total probability may error or look unstable—treat them as out of scope.
- Ill-conditioned inputs can magnify error in total probability far beyond display precision.
Important note
Educational engineering-mathematics tool. Verify critical designs with hand analysis or certified software.
How to Use This Calculator
- Enter the required values in the input fields.
- Click the Calculate button.
- View the computed result instantly.
Formula Used
Probability/statistics formula evaluation for Total Probability.. Probability/statistics formulas (mean, variance, common PMF/PDF models, regression) evaluated for the distribution or sample inputs this calculator accepts. This page targets specifically: Total Probability (total probability) (calculator id: total-probability-calculator).
Example Calculation
Example path for Total Probability: set event_a = 3, event_b = 2. Then compare the on-page result with a hand calculation using: Probability/statistics formula evaluation for Total Probability.. Probability/statistics formulas (mean, variance, common PMF/PDF models, regression) evaluated for the distribution or sample inputs this calculator accepts. This page targets specifically: Total Probability (total probability)..
Frequently Asked Questions
What is Total Probability Calculator?
- Total Probability Calculator evaluates Total Probability for the engineering-math / probability-random-variables library. Primary input cue: Event A Probability [required] — field id `event_a`. Method anchor: Probability/statistics formula evaluation for Total Probability.. Probability/statistics formulas (mean, variance, common PMF/PDF models, regression) evaluated .
How does Total Probability Calculator work?
- Probability/statistics formula evaluation for Total Probability.. Probability/statistics formulas (mean, variance, common PMF/PDF models, regression) evaluated for the distribution or sample inputs this calculator accepts. This page targets specifically: Total Probability (total probability) (calculator id: total-probability-calculator).
Why use this Math Numbers calculator?
- Use this page when you need total probability from known inputs and want a transparent arithmetic or symbolic check.