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Expected Value (Discrete) — result sheet
Mean outcome of a gamble or lottery from values and probabilities.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: E = sum(x_i * p_i).
Probability-weighted average: the long-run mean per play. Probabilities must each lie in [0,1] and sum to 1 within a tiny tolerance.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Outcome values — One per probability, same order.
- Matching probabilities — Each 0-1; must sum to 1.
Worked example
| Input | Value |
|---|---|
| Outcome values | 100, 0 |
| Matching probabilities | 0.2, 0.8 |
Expected value: 20.
Assumptions and limits
- Matched lists, at least 1 outcome.
- Probabilities sum to 1 (tolerance 1e-9).
- At most 1,000 outcomes.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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