Mathematics · Probability
Expected Value Calculator
Calculate the weighted mean of three possible outcomes.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- 0×0.5+10×0.3+20×0.2=7.
- Report Expected value=7, Probability total=1.
Understand Expected value
One idea, three depths
Choose how deeply to explain Expected value
Expected value: Calculate the weighted mean of three possible outcomes.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Expected value to answer this question: calculate the weighted mean of three possible outcomes? Enter Outcome 1, Probability 1, Outcome 2, and 3 other inputs; the calculator shows Expected value. For example: Outcomes 0,10,20 with probabilities .5,.3,.2 have expectation 7. The answer tells you Expected value.
Age 15Explain it to a 15-year-oldConnect it to the formula
Expected value is the long-run average under repeated trials. The rule is E[X]=Σxᵢpᵢ. Its input values are Outcome 1, Probability 1, Outcome 2, Probability 2, Outcome 3, Probability 3, and the main result is Expected value. For example: Outcomes 0,10,20 with probabilities .5,.3,.2 have expectation 7.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated expected value relation over the valid real-number domain stated below. The implemented relation is E[X]=Σxᵢpᵢ, evaluated from Outcome 1, Probability 1, Outcome 2, Probability 2, Outcome 3, Probability 3 to produce Expected value. Expected value is the long-run average under repeated trials. Probabilities must sum to one; expected value need not be a possible outcome.
Inputs and valid domain
- Outcome 1 must be a finite real number.
- Probability 1 must be a finite real number.
- Outcome 2 must be a finite real number.
- Probability 2 must be a finite real number.
- Outcome 3 must be a finite real number.
- Probability 3 must be a finite real number.
Important boundary: Probabilities must sum to one; expected value need not be a possible outcome.
The formula
E[X]=Σxᵢpᵢ
How the calculator works through it
It substitutes Outcome 1, Probability 1, Outcome 2, Probability 2, Outcome 3, Probability 3 into the formula and exposes every numerical step above. The main output is Expected value, accompanied by Probability total.
Read the result correctly
The Expected value is the direct answer to “calculate the weighted mean of three possible outcomes.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
Outcomes 0,10,20 with probabilities .5,.3,.2 have expectation 7.
Where this model stops being reliable
Probabilities must sum to one; expected value need not be a possible outcome.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Expected value works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Expected value uses E[X]=Σxᵢpᵢ. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Probability as a modelled proportion
Probability rules are needed to interpret what the Expected value result says about possible outcomes.
Review this foundation about 5 min
Optional enrichment
- Ordered arrangements
Counting ordered arrangements can extend Expected value to more detailed sample spaces and event models.
Review this foundation about 5 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read Outcome 1, Probability 1, Outcome 2, Probability 2, Outcome 3, Probability 3.
- Evaluate the principal relationship: E[X]=Σxᵢpᵢ.
- Return Expected value and check the domain conditions described above.
Python
from math import *
def expected_value_three(v1, v2, v3, v4, v5, v6) -> float:
return (((v1 * v2) + (v3 * v4)) + (v5 * v6))
assert abs(expected_value_three(0, 0.5, 10, 0.3, 20, 0.2) - 7) < 1e-6 * max(1.0, abs(7))
C
#include <assert.h>
#include <math.h>
double expected_value_three(double v1, double v2, double v3, double v4, double v5, double v6) {
return (((v1 * v2) + (v3 * v4)) + (v5 * v6));
}
int main(void) {
const double expected = 7;
const double actual = expected_value_three(0, 0.5, 10, 0.3, 20, 0.2);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double expected_value_three(double v1, double v2, double v3, double v4, double v5, double v6) {
return (((v1 * v2) + (v3 * v4)) + (v5 * v6));
}
int main() {
constexpr double expected = 7;
const double actual = expected_value_three(0, 0.5, 10, 0.3, 20, 0.2);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double expected_value_three(double v1, double v2, double v3, double v4, double v5, double v6)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global expected_value_three
section .text
expected_value_three:
push rbp
mov rbp, rsp
sub rsp, 96
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd [rbp-24], xmm2
movsd [rbp-32], xmm3
movsd [rbp-40], xmm4
movsd [rbp-48], xmm5
movsd xmm0, [rbp-8]
mulsd xmm0, [rbp-16]
movsd [rbp-72], xmm0
movsd xmm0, [rbp-24]
mulsd xmm0, [rbp-32]
movsd [rbp-80], xmm0
movsd xmm0, [rbp-72]
addsd xmm0, [rbp-80]
movsd [rbp-64], xmm0
movsd xmm0, [rbp-40]
mulsd xmm0, [rbp-48]
movsd [rbp-88], xmm0
movsd xmm0, [rbp-64]
addsd xmm0, [rbp-88]
movsd [rbp-56], xmm0
movsd xmm0, [rbp-56]
leave
ret
MATLAB
function result = expected_value_three(v1, v2, v3, v4, v5, v6)
result = (((v1 * v2) + (v3 * v4)) + (v5 * v6));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[v1_, v2_, v3_, v4_, v5_, v6_] := (((v1 * v2) + (v3 * v4)) + (v5 * v6));
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations
Standards, reading and academic references
Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.
Introductory Statistics 2e
Read the free OpenStax statistics textbookCite this book
- APA 7
- Illowsky, B., & Dean, S. (2023). Introductory statistics 2e. OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction
- MLA 9
- Illowsky, Barbara, and Susan Dean. Introductory Statistics 2e. OpenStax, 2023, https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
- Chicago author-date
- Illowsky, Barbara, and Susan Dean. 2023. Introductory Statistics 2e. Houston, TX: OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Expected Value Calculator. MW SysArc Tools. https://math.mwsysarc.com/probability/expected-value-three-outcomes
MLA 9
MW SysArc. “Expected Value Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/probability/expected-value-three-outcomes. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Expected Value Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/probability/expected-value-three-outcomes.
Harvard
MW SysArc (2026) ‘Expected Value Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/probability/expected-value-three-outcomes (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_expected_value_three_2026,
author = {{MW SysArc}},
title = {Expected Value Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/probability/expected-value-three-outcomes},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Expected Value Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/probability/expected-value-three-outcomes
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Expected value do?
Calculate the weighted mean of three possible outcomes.
How does the Expected value work?
The calculator applies E[X]=Σxᵢpᵢ. Expected value is the long-run average under repeated trials.
What can I learn from the Expected value?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .