Expected Value (EV) is a fundamental concept in probability and statistics, representing the weighted average of all possible outcomes of a random variable. It's calculated by multiplying each possible outcome by its probability and then summing up these products. In simpler terms, it tells you what you can expect to gain or lose on average over a large number of trials.
The formula for Expected Value is:
E(X) = Σ [ P(xᵢ) * xᵢ ]
Where:
E(X) is the Expected Value of the random variable X.
Σ denotes the sum of all elements.
P(xᵢ) is the probability of the i-th outcome.
xᵢ is the value of the i-th outcome.
Use Cases:
Gambling and Games: Determining if a bet or game has a positive or negative expected value, indicating long-term profitability or loss.
Investment Decisions: Evaluating potential investment opportunities by considering the possible returns and their likelihoods.
Insurance: Calculating premiums by estimating the expected payouts for claims.
Business Strategy: Making decisions under uncertainty by forecasting potential profits or losses from different strategies.
Decision Making: Assisting in choices where outcomes are uncertain but probabilities can be estimated.
How the Calculator Works:
This calculator allows you to input the value of each possible outcome and its corresponding probability. The probability should be entered as a decimal between 0 and 1 (e.g., 0.5 for 50%). After entering all outcomes and their probabilities, click the "Calculate Expected Value" button. The calculator will then apply the formula E(X) = Σ [ P(xᵢ) * xᵢ ] and display the resulting expected value. Ensure that the sum of all probabilities equals 1 (or very close to 1 due to rounding) for accurate results, although the calculator will function with probabilities that don't sum to 1, it's a good practice for a complete probability distribution.
var outcomeCounter = 2; // Start with 2 pre-filled outcomes
function addOutcome() {
outcomeCounter++;
var outcomesContainer = document.getElementById("outcomesContainer");
var newOutcomeRow = document.createElement("div");
newOutcomeRow.className = "outcome-row";
newOutcomeRow.innerHTML =
'' +
" +
'' +
" +
'';
outcomesContainer.appendChild(newOutcomeRow);
}
function removeOutcome(button) {
var rowToRemove = button.parentNode;
rowToRemove.parentNode.removeChild(rowToRemove);
}
function calculateExpectedValue() {
var totalExpectedValue = 0;
var probabilitySum = 0;
var outcomeElements = document.querySelectorAll('.outcome-row');
for (var i = 0; i < outcomeElements.length; i++) {
var valueInput = outcomeElements[i].querySelector('input[type="number"]');
var probabilityInput = outcomeElements[i].querySelector('.probability-input');
var outcomeValue = parseFloat(valueInput.value);
var outcomeProbability = parseFloat(probabilityInput.value);
// Basic validation: Ensure inputs are numbers and probability is between 0 and 1
if (isNaN(outcomeValue) || isNaN(outcomeProbability)) {
alert('Please enter valid numbers for all outcomes and probabilities.');
return;
}
if (outcomeProbability 1) {
alert('Probabilities must be between 0 and 1.');
return;
}
totalExpectedValue += outcomeValue * outcomeProbability;
probabilitySum += outcomeProbability;
}
// Optional: Check if probabilities sum to 1
if (Math.abs(probabilitySum – 1) > 0.001) { // Allow for minor floating point inaccuracies
console.warn("Warning: Probabilities do not sum to 1. Sum is: " + probabilitySum);
// Decide if you want to alert the user or just proceed
// alert("Warning: Probabilities do not sum to 1. Results may be misleading.");
}
var resultDisplay = document.getElementById('expectedValueResult');
if (isNaN(totalExpectedValue)) {
resultDisplay.textContent = 'Error';
} else {
// Format the output, potentially to a few decimal places
resultDisplay.textContent = totalExpectedValue.toFixed(4);
}
}